Author name code: weiss
ADS astronomy entries on 2022-09-14
author:"Weiss, Nigel O."
------------------------------------------------------------------------  

Title: On long-term modulation of the Sun's magnetic cycle
Authors: Beer, J.; Tobias, S. M.; Weiss, N. O.
Bibcode: 2018MNRAS.473.1596B
Altcode:
  We utilize reconstructions based on cosmogenic radionuclides as well
  as direct observations of solar magnetic activity, to argue that
  the solar dynamo has operated similarly to the present day for at
  least the past 10 000 yr. The persistence of the 87-yr Gleissberg
  cycle throughout supermodulation events suggests that the Hale and
  Schwabe cycles continue independently of the modulational mechanism
  for activity. We further analyse behaviour of solar activity during
  the Spörer and Maunder Minima. Such grand minima recur with the
  characteristic de Vries period of approximately 208 yr but their
  incidence is modulated by the Hallstatt cycle with a characteristic
  period of around 2300 yr. We ascribe the latter to supermodulation,
  caused by breaking the symmetry of the dynamo pattern. Finally, we
  emphasize the need for further calculations in order to determine the
  effects of changes in solar field morphology and symmetry on the solar
  wind and on cosmic ray deflection.

Title: Supermodulation of the Sun's magnetic activity: the effects
    of symmetry changes
Authors: Weiss, N. O.; Tobias, S. M.
Bibcode: 2016MNRAS.456.2654W
Altcode:
  In this paper, we argue that the solar activity record, as revealed by
  telescopic observations and proxy data from the abundances of cosmogenic
  isotopes, is consistent with the action of a deterministic non-linear
  chaotic dynamo. In particular, we claim that the long time-scale
  `supermodulation' apparent in the isotopic record can be ascribed to
  switching of the dynamo between two different modulational patterns. The
  first (which is currently in operation) involves deep grand minima and
  occasional changes in symmetry triggered by these minima. The second,
  which exhibits only weak modulation and no grand minima, arises as
  a consequence of symmetry breaking. These processes are demonstrated
  for highly idealized simple models of the non-linear dynamo equations.

Title: Solar Activity in the Past and the Chaotic Behaviour of
    the Dynamo
Authors: Arlt, Rainer; Weiss, Nigel
Bibcode: 2015sac..book..525A
Altcode:
  No abstract at ADS

Title: Solar Activity in the Past and the Chaotic Behaviour of
    the Dynamo
Authors: Arlt, Rainer; Weiss, Nigel
Bibcode: 2014SSRv..186..525A
Altcode: 2014SSRv..tmp...27A; 2014arXiv1406.7628A
  The record of solar activity is reviewed here with emphasis on
  peculiarities. Since sunspot positions tell us a lot more about the
  solar dynamo than the various global sunspot numbers, we first focus on
  the records of telescopic observations of sunspots leading to positional
  information. Then we turn to the proxy record from cosmogenic isotope
  abundances, which shows recurrent grand minima over the last 9500
  years. The apparent distinction between episodes of strong modulation,
  and intervening episodes with milder modulation and weaker overall
  activity, hints at the solar dynamo following a variety of solutions,
  with different symmetries, over the course of millennia.

Title: Sunspots and Starspots
Authors: Thomas, John H.; Weiss, Nigel O.
Bibcode: 2012sust.book.....T
Altcode:
  Preface; 1. The sun among the stars; 2. Sunspots and starspots:
  a historical introduction; 3. Overall structure of a sunspot;
  4. Fine structure of the umbra; 5. Fine structure of the penumbra;
  6. Oscillations in sunspots; 7. Sunspots and active regions; 8. Magnetic
  activity in stars; 9. Starspots; 10. Solar and stellar activity cycles;
  11. Solar and stellar dynamos; 12. Solar activity, space weather,
  and climate change; 13. The way ahead; Appendices; References; Index.

Title: Convectively driven dynamo action in the quiet Sun
Authors: Bushby, P. J.; Favier, B.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 2012GApFD.106..508B
Altcode:
  Observations of the quiet solar surface indicate that localised
  concentrations of vertical magnetic flux tend to accumulate in the
  convective downflows. Furthermore, there is some evidence to suggest
  that mesogranular boundaries are preferred locations for the formation
  of these flux concentrations. This implies that these magnetic fields
  are organised on scales that are larger than the granular scale. One
  possible explanation for the existence of quiet Sun magnetic features is
  that they are continuously regenerated by the near-surface convective
  motions. Motivated by this, we consider dynamo action in a local
  Cartesian model of convection in a compressible electrically conducting
  fluid. The horizontal scale of this domain is large enough to model
  mesoscale behaviour. Dynamo action occurs provided that the magnetic
  Reynolds number exceeds some critical value. In the kinematic regime
  the presence of mesogranules seems to be beneficial for dynamo action:
  compared to similar smaller aspect ratio calculations, we find higher
  kinematic growth rates for the magnetic energy, as well as a lower
  value for the critical magnetic Reynolds number. In the nonlinear
  regime the peak magnetic field strengths compare very favourably
  to observations, greatly exceeding the equipartition value at the
  surface, as observed in the quiet Sun. However, there is no evidence
  to suggest that the presence of mesogranules significantly increases
  the saturation level of the dynamo in this nonlinear regime, which
  (in the highest magnetic Reynolds number case) is comparable to that
  found in similar calculations in smaller domains.

Title: Reflections on magnetoconvection
Authors: Weiss, N. O.
Bibcode: 2012GApFD.106..353W
Altcode:
  The interaction between magnetic fields and convection can be observed
  directly in stars like the Sun. This selective review uses idealized
  numerical experiments to illustrate and extend results obtained
  from bifurcation theory. It covers a wide variety of steady and
  time-dependent behaviour, in incompressible and compressible fluids,
  in two and three dimensions. These results illuminate behaviour that
  appears in recent "realistic" simulations of solar magnetoconvection.

Title: Magnetic buoyancy instabilities in the presence of magnetic
    flux pumping at the base of the solar convection zone
Authors: Barker, Adrian J.; Silvers, Lara J.; Proctor, Michael R. E.;
   Weiss, Nigel O.
Bibcode: 2012MNRAS.424..115B
Altcode: 2012arXiv1204.5432B
  We perform idealized numerical simulations of magnetic buoyancy
  instabilities in three dimensions, solving the equations
  of compressible magnetohydrodynamics in a model of the solar
  tachocline. In particular, we study the effects of including a
  highly simplified model of magnetic flux pumping in an upper layer
  ('the convection zone') on magnetic buoyancy instabilities in a lower
  layer ('the upper parts of the radiative interior - including the
  tachocline'), to study these competing flux transport mechanisms at
  the base of the convection zone. The results of the inclusion of this
  effect in numerical simulations of the buoyancy instability of both a
  preconceived magnetic slab and a shear-generated magnetic layer are
  presented. In the former, we find that if we are in the regime that
  the downward pumping velocity is comparable with the Alfvén speed of
  the magnetic layer, magnetic flux pumping is able to hold back the
  bulk of the magnetic field, with only small pockets of strong field
  able to rise into the upper layer. <P />In simulations in which the
  magnetic layer is generated by shear, we find that the shear velocity
  is not necessarily required to exceed that of the pumping (therefore
  the kinetic energy of the shear is not required to exceed that of the
  overlying convection) for strong localized pockets of magnetic field
  to be produced which can rise into the upper layer. This is because
  magnetic flux pumping acts to store the field below the interface,
  allowing it to be amplified both by the shear and by vortical fluid
  motions, until pockets of field can achieve sufficient strength to
  rise into the upper layer. In addition, we find that the interface
  between the two layers is a natural location for the production of
  strong vertical gradients in the magnetic field. If these gradients
  are sufficiently strong to allow the development of magnetic buoyancy
  instabilities, strong shear is not necessarily required to drive them
  (cf. previous work by Vasil &amp; Brummell). We find that the addition
  of magnetic flux pumping appears to be able to assist shear-driven
  magnetic buoyancy in producing strong flux concentrations that can
  rise up into the convection zone from the radiative interior.

Title: The Solar Tachocline
Authors: Hughes, D. W.; Rosner, R.; Weiss, N. O.
Bibcode: 2012sota.book.....H
Altcode:
  Preface; Part I. Setting the Scene: 1. An introduction to the solar
  tachocline D. O. Gough; 2. Reflections on the solar tachocline
  E. A. Spiegel; Part II. Observations: 3. Observational results
  and issues concerning the tachocline J. Christensen-Dalsgaard and
  M. J. Thompson; Part III. Hydrodynamic Models: 4. Hydrodynamic models of
  the tachocline J.-P. Zahn; 5. Turbulence in the tachocline M. S. Miesch;
  6. Mean field modelling of differential rotation G. Rudiger and
  L. L. Kitchatinov; Part IV. Hydromagnetic Properties: 7. Magnetic
  confinement of the solar tachocline P. Garaud; 8. Magnetic confinement
  and the sharp tachopause M. E. McIntyre; 9. ß-Plane MHD turbulence
  and dissipation in the solar tachocline P. H. Diamond, K. Itoh,
  S.-I. Itoh and L. J. Silvers; Part V. Instabilities: 10. Global
  MHD instabilities of the tachocline P. A. Gilman and P. S. Cally;
  11. Magnetic buoyancy instabilities in the tachocline D. W. Hughes;
  12. Instabilities, angular momentum transport and magnetohydrodynamic
  turbulence G. I. Ogilvie; Part VI. Dynamo Action: 13. The solar dynamo
  and the tachocline S. M. Tobias and N. O. Weiss; Part VII. Overview:
  14. On studying the rotating solar interior R. Rosner; Index.

Title: Global model of differential rotation in the Sun
Authors: Balbus, Steven A.; Latter, Henrik; Weiss, Nigel
Bibcode: 2012MNRAS.420.2457B
Altcode: 2011arXiv1111.3809B
  The isorotation contours of the solar convective zone (SCZ) show three
  distinct morphologies, corresponding to two boundary layers (inner and
  outer), and the bulk of the interior. Previous work has shown that the
  thermal wind equation (TWE) together with informal arguments on the
  nature of convection in a rotating fluid could be used to deduce the
  shape of the isorotation surfaces in the bulk of the SCZ with great
  fidelity, and that the tachocline contours could also be described by
  relatively simple phenomenology. In this paper, we show that the form
  of these surfaces can be understood more broadly as a mathematical
  consequence of the TWE and a narrow convective shell. The analysis
  does not yield the angular velocity function directly; an additional
  surface boundary condition is required. However, much can already
  be deduced without constructing the entire rotation profile. The
  mathematics may be combined with dynamical arguments put forth in
  previous works to the mutual benefit of each. An important element of
  our approach is to regard the constant angular velocity surfaces as
  an independent coordinate variable for what is termed the 'residual
  entropy', a quantity that plays a key role in the equation of thermal
  wind balance. The difference between the dynamics of the bulk of the
  SCZ and the tachocline is due to a different functional form of the
  residual entropy in each region. We develop a unified theory for the
  rotational behaviour of both the SCZ and the tachocline, using the
  solutions for the characteristics of the TWE. These characteristics
  are identical to the isorotation contours in the bulk of the SCZ,
  but the two deviate in the tachocline. The outer layer may be treated,
  at least descriptively, by similar mathematical techniques, but this
  region probably does not obey thermal wind balance.

Title: Solar and Stellar Dynamos
Authors: Weiss, Nigel O.
Bibcode: 2011IAUS..271..247W
Altcode:
  Records of the solar magnetic field extend back for millennia,
  and its surface properties have been observed for centuries, while
  helioseismology has recently revealed the Sun's internal rotation and
  the presence of a tachocline. Dynamo theory has developed to explain
  these observations, first with idealized models based on mean-field
  electrodynamics and, more recently, by direct numerical simulation,
  notably with the ASH code at Boulder. These results, which suggest
  that cyclic activity relies on the presence of the tachocline, and that
  its modulation is chaotic (rather than stochastic), will be critically
  reviewed. Similar theoretical approaches have been followed in order
  to explain the magnetic properties of other main-sequence stars,
  whose fields can be mapped by Zeeman-Doppler imaging. Of particular
  interest is the behaviour of fully convective, low-mass stars, which
  lack any tachocline but are nevertheless extremely active.

Title: The influence of stratification upon small-scale
    convectively-driven dynamos
Authors: Bushby, Paul J.; Proctor, Michael R. E.; Weiss, Nigel O.
Bibcode: 2011IAUS..271..197B
Altcode:
  In the quiet Sun, convective motions form a characteristic granular
  pattern, with broad upflows enclosed by a network of narrow
  downflows. Magnetic fields tend to accumulate in the intergranular
  lanes, forming localised flux concentrations. One of the most plausible
  explanations for the appearance of these quiet Sun magnetic features
  is that they are generated and maintained by dynamo action resulting
  from the local convective motions at the surface of the Sun. Motivated
  by this idea, we describe high resolution numerical simulations of
  nonlinear dynamo action in a (fully) compressible, non-rotating layer of
  electrically-conducting fluid. The dynamo properties depend crucially
  upon various aspects of the fluid. For example, the magnetic Reynolds
  number (Rm) determines the initial growth rate of the magnetic energy,
  as well as the final saturation level of the dynamo in the nonlinear
  regime. We focus particularly upon the ways in which the Rm-dependence
  of the dynamo is influenced by the level of stratification within
  the domain. Our results can be related, in a qualitative sense, to
  solar observations.

Title: Chaotic behaviour in low-order models of planetary and
    stellar dynamos
Authors: Weiss, N. O.
Bibcode: 2011GApFD.105..256W
Altcode:
  The behaviour of the geodynamo and the solar cycle can be modelled
  by low-order systems of coupled nonlinear differential equations. The
  Earth's magnetic field reverses aperiodically, and similar behaviour
  is exhibited by disc dynamos that are described by the Lorenz
  equations. Chaotic behaviour is also a characteristic feature of
  coupled disc dynamos. In stars like the Sun, magnetic activity varies
  cyclically, with regular reversals of magnetic fields, but the cyclic
  activity is modulated on longer timescales. This behaviour can be
  described by normal form equations that account for symmetry-breaking
  as well as for variations in amplitude. The Von Kármán Sodium
  (VKS) experiment has successfully demonstrated magnetic reversals
  in the laboratory, and these results can be represented by evolution
  equations also.

Title: Effects of boundary conditions on the onset of convection
    with tilted magnetic field and rotation vectors
Authors: Proctor, M. R. E.; Weiss, N. O.; Thompson, S. D.; Roxburgh,
   N. T.
Bibcode: 2011GApFD.105...82P
Altcode:
  The problem of the onset of thermal convection is considered, firstly
  when a uniform tilted magnetic field is present, and secondly in a frame
  rotating about an oblique axis. If up-down symmetry is broken we expect
  to find only bifurcations that lead to travelling waves. Numerical
  studies show, however, that in a Boussinesq fluid the spectrum of
  eigenvalues can be symmetrical about the real axis, even when the
  boundary conditions are asymmetrical. Here we show analytically that
  this symmetry property indeed holds for a wide range of boundary
  conditions and hence that both steady solutions and standing waves
  are allowed.

Title: Small-scale Dynamo Action in Compressible Convection
Authors: Bushby, P. J.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 2010ASPC..429..181B
Altcode:
  Motivated by observations of magnetic fields at the surface of the
  Sun, we consider direct numerical simulations of dynamo action in
  highly-stratified, three-dimensional compressible convection. Whether
  or not a convective flow can drive a dynamo depends crucially upon
  the magnetic Reynolds number. If this parameter is large enough that
  the inductive effects of the fluid motions outweigh the dissipative
  effects of magnetic diffusion, then dynamo action can occur. Simulating
  convection with a Reynolds number of approximately 150, we find that
  it is possible to excite a dynamo with computationally accessible
  values of the magnetic Reynolds number. In the kinematic regime,
  the growth rate of the dynamo has a logarithmic dependence upon the
  magnetic Reynolds number. Following these dynamos into the nonlinear
  regime, we find that intense, partially-evacuated concentrations of
  vertical magnetic flux form near the upper surface of the computational
  domain. This partial evacuation has a profound influence upon the
  efficiency of the (explicit) numerical scheme that is used in these
  calculations. These results can be related (in a qualitative sense)
  to recent observations of magnetic fields in the quiet Sun.

Title: Modulation of the sunspot cycle
Authors: Weiss, Nigel
Bibcode: 2010A&G....51c...9W
Altcode:
  Solar activity has been abnormally high for the last half-century,
  but the extremely feeble start of the latest 11-year cycle suggests
  that this episode is probably coming to an end. This prospect raises
  some fascinating and important issues, involving an extremely wide
  range of timescales, writes Nigel Weiss.

Title: Differential rotation in fully convective stars
Authors: Balbus, Steven A.; Weiss, Nigel O.
Bibcode: 2010MNRAS.404.1263B
Altcode: 2010MNRAS.tmp..279B; 2010arXiv1001.3542B
  Under the assumption of thermal wind balance and effective entropy
  mixing in constant rotation surfaces, the isorotational contours of the
  solar convective zone may be reproduced with great fidelity. Even at
  this early stage of development, this helioseismology fit may be used
  to put a lower bound on the mid-latitude radial solar entropy gradient,
  which is in good accord with standard mixing length theory. In this
  paper, we generalize this solar calculation to fully convective stars
  (and potentially planets), retaining the assumptions of thermal wind
  balance and effective entropy mixing in isorotational surfaces. It
  is found that each isorotation contour is of the form R<SUP>2</SUP>
  = A + BΦ(r), where R is the radius from the rotation axis, Φ(r)
  is the (assumed spherical) gravitational potential, and A and B
  are constants along the contour. This result is applied to simple
  models of fully convective stars. Both solar-like surface rotation
  profiles (angular velocity decreasing toward the poles) as well as
  `antisolar' profiles (angular velocity increasing toward the poles)
  are modelled; the latter bear some suggestive resemblance to numerical
  simulations. We also perform exploratory studies of zonal surface
  flows similar to those seen in Jupiter and Saturn. In addition to
  providing a practical framework for understanding the results of
  large-scale numerical simulations, our findings may also prove useful
  in dynamical calculations for which a simple but viable model for the
  background rotation profile in a convecting fluid is needed. Finally,
  our work bears directly on an important goal of the CoRoT programme:
  to elucidate the internal structure of rotating, convecting stars.

Title: Summary and Perspective
Authors: Weiss, N. O.
Bibcode: 2010ASSP...19..346W
Altcode: 2010mcia.conf..346W
  This meeting celebrated a double anniversary. A 100 years ago, George
  Ellery Hale had a hunch: he had noticed the vortical structure in Hα
  above sunspots, and he interpreted this as evidence for a vortex flow,
  which (he supposed) carried electric charges round a spot, and so
  provided an azimuthal electric current that would generate a magnetic
  field like that in a solenoid (Hale 1908a). His hunch was actually
  wrong since (as we now know) the solar plasma is electrically neutral
  - but when he looked for spectroscopic evidence of a magnetic field,
  using the recently discovered Zeeman effect, he found that there were
  kilogauss magnetic fields in sunspots (Hale 1908b). This was the first
  demonstration that magnetic fields were present outside the earth.

Title: Differential rotation and convection in the Sun
Authors: Balbus, Steven A.; Bonart, Julius; Latter, Henrik N.; Weiss,
   Nigel O.
Bibcode: 2009MNRAS.400..176B
Altcode: 2009arXiv0907.5075B
  We show that the differential rotation profile of the solar convection
  zone, apart from inner and outer boundary layers, can be reproduced with
  great accuracy if the isorotation contours correspond to characteristics
  of the thermal wind equation. This requires that there be a formal
  quantitative relationship involving the entropy and the angular
  velocity. Earlier work has suggested that this could arise from
  magnetohydrodynamic stability constraints; here, we argue that purely
  hydrodynamical processes could also lead to such a result. Of special
  importance to the hydrodynamical solution is the fact that the thermal
  wind equation is insensitive to radial entropy gradients. This allows
  a much more general class of solutions to fit the solar isorotation
  contours, beyond just those in which the entropy itself must be a
  function of the angular velocity. In particular, for this expanded
  class, the thermal wind solution of the solar rotation profile remains
  valid even when large radial entropy gradients are present. A clear
  and explicit example of this class of solution appears to be present
  in published numerical simulations of the solar convective zone. Though
  hydrodynamical in character, the theory is not sensitive to the presence
  of weak magnetic fields. Thus, the identification of solar isorotation
  contours with the characteristics of the thermal wind equation appears
  to be robust, accommodating, but by no means requiring, magnetic
  field dynamics.

Title: The Solar Dynamo
Authors: Weiss, N. O.; Thompson, M. J.
Bibcode: 2009SSRv..144...53W
Altcode: 2008SSRv..tmp..155W
  It is generally accepted that the strong toroidal magnetic fields that
  emerge through the solar surface in sunspots and active regions are
  formed by the action of differential rotation on a poloidal field,
  and then stored in or near the tachocline at the base of the Sun’s
  convection zone. The problem is how to explain the generation of
  a reversed poloidal field from this toroidal flux—a process that
  can be parametrised in terms of an α-effect related to some form
  of turbulent helicity. Here we first outline the principal patterns
  that have to be explained: the 11-year activity cycle, the 22-year
  magnetic cycle and the longer term modulation of cyclic activity,
  associated with grand maxima and minima. Then we summarise what has
  been learnt from helioseismology about the Sun’s internal structure
  and rotation that may be relevant to our subject. The ingredients
  of mean-field dynamo models are differential rotation, meridional
  circulation, turbulent diffusion, flux pumping and the α-effect:
  in various combinations they can reproduce the principal features
  that are observed. To proceed further, it is necessary to rely on
  large-scale computation and we summarise the current state of play.

Title: The Solar Dynamo
Authors: Weiss, N. O.; Thompson, M. J.
Bibcode: 2009odsm.book...53W
Altcode:
  It is generally accepted that the strong toroidal magnetic fields that
  emerge through the solar surface in sunspots and active regions are
  formed by the action of differential rotation on a poloidal field,
  and then stored in or near the tachocline at the base of the Sun's
  convection zone. The problem is how to explain the generation of
  a reversed poloidal field from this toroidal flux—a process that
  can be parametrised in terms of an α-effect related to some form
  of turbulent helicity. Here we first outline the principal patterns
  that have to be explained: the 11-year activity cycle, the 22-year
  magnetic cycle and the longer term modulation of cyclic activity,
  associated with grand maxima and minima. Then we summarise what has
  been learnt from helioseismology about the Sun's internal structure
  and rotation that may be relevant to our subject. The ingredients
  of mean-field dynamo models are differential rotation, meridional
  circulation, turbulent diffusion, flux pumping and the α-effect:
  in various combinations they can reproduce the principal features
  that are observed. To proceed further, it is necessary to rely on
  large-scale computation and we summarise the current state of play.

Title: Oded Regev (2006): Chaos and Complexity in
    Astrophysics. Cambridge University Press, 468 pp., $89. ISBN-13
    978-0-521-85534-1 (ISBN-10 0-521-85534-9)
Authors: Weiss, Nigel
Bibcode: 2008ThCFD..22..485W
Altcode: 2008ThCFD.tmp...16W
  No abstract at ADS

Title: Sunspots and Starspots
Authors: Thomas, John H.; Weiss, Nigel O.
Bibcode: 2008sust.book.....T
Altcode:
  Preface; 1. The sun among the stars; 2. Sunspots and starspots:
  a historical introduction; 3. Overall structure of a sunspot;
  4. Fine structure of the umbra; 5. Fine structure of the penumbra;
  6. Oscillations in sunspots; 7. Sunspots and active regions; 8. Magnetic
  activity in stars; 9. Starspots; 10. Solar and stellar activity cycles;
  11. Solar and stellar dynamos; 12. Solar activity, space weather,
  and climate change; 13. The way ahead; Appendices; References; Index.

Title: For how long will the current grand maximum of solar activity
    persist?
Authors: Abreu, J. A.; Beer, J.; Steinhilber, F.; Tobias, S. M.;
   Weiss, N. O.
Bibcode: 2008GeoRL..3520109A
Altcode:
  Understanding the Sun's magnetic activity is important because of its
  impact on the Earth's environment. The sunspot record since 1610 shows
  irregular 11-year cycles of activity; they are modulated on longer
  timescales and were interrupted by the Maunder minimum in the 17th
  century. Future behavior cannot easily be predicted - even in the
  short-term. Recent activity has been abnormally high for at least
  8 cycles: is this grand maximum likely to terminate soon or even to
  be followed by another (Maunder-like) grand minimum? To answer these
  questions we use, as a measure of the Sun's open magnetic field, a
  composite record of the solar modulation function Φ, reconstructed
  principally from the proxy record of cosmogenic <SUP>10</SUP>Be
  abundances in the GRIP icecore from Greenland. This Φ record extends
  back for almost 10,000 years, showing many grand maxima and grand
  minima (defined as intervals when Φ is within the top or bottom 20%
  of a Gaussian distribution). We carry out a statistical analysis of
  this record and calculate the life expectancy of the current grand
  maximum. We find that it is only expected to last for a further 15-36
  years, with the more reliable methods yielding shorter expectancies,
  and we therefore predict a decline in solar activity within the next
  two or three cycles. We are not able, however, to predict the level
  of the ensuing minimum.

Title: Flux Pumping and Magnetic Fields in the Outer Penumbra of
    a Sunspot
Authors: Brummell, Nicholas H.; Tobias, Steven M.; Thomas, John H.;
   Weiss, Nigel O.
Bibcode: 2008ApJ...686.1454B
Altcode:
  The filamentary structure of a sunspot penumbra is believed to be
  magnetoconvective in origin. In the outer penumbra there is a difference
  in inclination of up to 30°-40° between the magnetic fields associated
  with bright and dark filaments, and the latter fields plunge downward
  below the surface toward the edge of the spot. We have proposed that
  these fields are dragged downward by magnetic pumping caused by the
  external granular convection. In this paper we model this process in
  a more elaborate idealized configuration that includes the curvature
  force exerted by an arched magnetic field in addition to magnetic
  buoyancy, and demonstrate that magnetic pumping remains an efficient
  mechanism for holding flux submerged. We discuss the implications of
  these results for the magnetic structure of the outer penumbra.

Title: Convective intensification of magnetic fields in the quiet Sun
Authors: Bushby, P. J.; Houghton, S. M.; Proctor, M. R. E.; Weiss,
   N. O.
Bibcode: 2008MNRAS.387..698B
Altcode: 2008arXiv0804.1238B
  Kilogauss-strength magnetic fields are often observed in intergranular
  lanes at the photosphere in the quiet Sun. Such fields are stronger
  than the equipartition field B<SUB>e</SUB>, corresponding to a
  magnetic energy density that matches the kinetic energy density of
  photospheric convection, and comparable with the field B<SUB>p</SUB>
  that exerts a magnetic pressure equal to the ambient gas pressure. We
  present an idealized numerical model of three-dimensional compressible
  magnetoconvection at the photosphere, for a range of values of the
  magnetic Reynolds number. In the absence of a magnetic field, the
  convection is highly supercritical and characterized by a pattern of
  vigorous, time-dependent, `granular' motions. When a weak magnetic
  field is imposed upon the convection, magnetic flux is swept into the
  convective downflows where it forms localized concentrations. Unless
  this process is significantly inhibited by magnetic diffusion, the
  resulting fields are often much greater than B<SUB>e</SUB> and the high
  magnetic pressure in these flux elements leads to their being partially
  evacuated. Some of these flux elements contains ultraintense magnetic
  fields that are significantly greater than B<SUB>p</SUB>. Such fields
  are contained by a combination of the thermal pressure of the gas and
  the dynamic pressure of the convective motion, and they are constantly
  evolving. These ultraintense fields develop owing to non-linear
  interactions between magnetic fields and convection; they cannot be
  explained in terms of `convective collapse' within a thin flux tube
  that remains in overall pressure equilibrium with its surroundings.

Title: Convection-driven Emergence of Small-Scale Magnetic Fields
    and their Role in Coronal Heating and Solar Wind Acceleration
Authors: Isobe, H.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 2008ApJ...679L..57I
Altcode:
  Recent observations by the Solar Optical Telescope (SOT) on board
  Hinode have revealed that the surface of the Sun is, on average,
  covered with small-scale horizontal magnetic fields. Frequent emergence
  of horizontal magnetic flux on a granular scale is found in the quiet
  Sun and in plage regions. In this Letter we present the results of
  magnetohydrodynamic simulations that cover the upper convection zone
  and the corona. It is found that, even when the initial magnetic field
  is uniform and vertical, a disordered magnetic field is produced in the
  convection zone. The photospheric magnetic field is then characterized
  by strong vertical fields concentrated in the intergranular lanes and
  relatively weak, horizontal fields both in the granules and in the
  intergranular lanes. Occasionally, fragments with large magnetic fluxes
  are driven above the photosphere by the upward convective flows. These
  characteristics are consistent with the SOT observations. Moreover,
  the simulated flux emerging on a granular scale undergoes magnetic
  reconnection with the expanding vertical magnetic concentrations in the
  chromosphere. These reconnection events heat the local plasma and emit
  high-frequency waves that propagate into the corona. Such an interplay
  between the small-scale horizontal fields and the vertical flux may
  play an important role in coronal heating and wind acceleration in
  the Sun and stars.

Title: The Solar Tachocline
Authors: Hughes, D. W.; Rosner, R.; Weiss, N. O.
Bibcode: 2007sota.book.....H
Altcode:
  Preface; Part I. Setting the Scene: 1. An introduction to the solar
  tachocline D. O. Gough; 2. Reflections on the solar tachocline
  E. A. Spiegel; Part II. Observations: 3. Observational results
  and issues concerning the tachocline J. Christensen-Dalsgaard and
  M. J. Thompson; Part III. Hydrodynamic Models: 4. Hydrodynamic models of
  the tachocline J.-P. Zahn; 5. Turbulence in the tachocline M. S. Miesch;
  6. Mean field modelling of differential rotation G. Rudiger and
  L. L. Kitchatinov; Part IV. Hydromagnetic Properties: 7. Magnetic
  confinement of the solar tachocline P. Garaud; 8. Magnetic confinement
  and the sharp tachopause M. E. McIntyre; 9. ß-Plane MHD turbulence
  and dissipation in the solar tachocline P. H. Diamond, K. Itoh,
  S.-I. Itoh and L. J. Silvers; Part V. Instabilities: 10. Global
  MHD instabilities of the tachocline P. A. Gilman and P. S. Cally;
  11. Magnetic buoyancy instabilities in the tachocline D. W. Hughes;
  12. Instabilities, angular momentum transport and magnetohydrodynamic
  turbulence G. I. Ogilvie; Part VI. Dynamo Action: 13. The solar dynamo
  and the tachocline S. M. Tobias and N. O. Weiss; Part VII. Overview:
  14. On studying the rotating solar interior R. Rosner; Index.

Title: Sunspot Structure and Dynamics
Authors: Weiss, N. O.
Bibcode: 2007sdeh.book...13W
Altcode:
  No abstract at ADS

Title: The Solar Tachocline
Authors: Hughes, David W.; Rosner, Robert; Weiss, Nigel O.
Bibcode: 2007sota.conf.....H
Altcode:
  No abstract at ADS

Title: The solar dynamo and the tachocline
Authors: Tobias, Steven; Weiss, Nigel
Bibcode: 2007sota.conf..319T
Altcode:
  No abstract at ADS

Title: The Puzzling Structure of a Sunspot
Authors: Weiss, N. O.
Bibcode: 2006ASPC..354..213W
Altcode:
  Sunspots are characterized by the presence of a filamentary penumbra
  but it is only within the last few years that the fine structure of
  penumbral magnetic fields, and of the associated Evershed outflow,
  has been definitively established. High resolution observations show
  that bright filaments in the inner penumbra possess slender dark cores
  with fields and flows that are nearly horizontal, while the ambient
  fields are inclined at 40° to the vertical. In the outer penumbra
  the fields in bright and dark filaments differ in inclination by
  about 30° and recent observations confirm that the Evershed flow is
  along the almost horizontal fields in dark filaments. Moreover, these
  two families of field lines remain distinct. This intricate magnetic
  geometry poses major theoretical problems. How can such a structure be
  maintained and how does it originate? How do penumbral fields relate
  to the photospheric granulation outside the spot? What drives the
  Evershed flow within dark filaments? What form does convection take
  in the umbra, in bright filaments and in dark filaments? What causes
  the fine structure within bright filaments? What is the subsurface
  structure of a sunspot and how does it relate to outflows and inflows
  in the moat cell that surrounds it? Although a general theoretical
  picture is beginning to emerge, these questions can only be properly
  answered through detailed computational investigations, guided by
  further observations both from the ground and from space.

Title: Unpredictable Sun leaves researchers in the dark
Authors: Tobias, Steven; Hughes, David; Weiss, Nigel
Bibcode: 2006Natur.442...26T
Altcode:
  No abstract at ADS

Title: On the fine structure of magnetic fields in sunspot penumbrae
Authors: Thomas, J. H.; Weiss, N. O.; Tobias, S. M.; Brummell, N. H.
Bibcode: 2006A&A...452.1089T
Altcode:
  Recent observations have revealed the interlocking-comb structure of
  the magnetic field in the outer penumbra of a sunspot. We have argued
  that this structure owes its origin in part to downward pumping of
  magnetic flux by vigorous granular convection in the region surrounding
  the spot. Here we stress the difference between the inner and outer
  penumbra, and correct some misleading assertions in a recent paper by
  Spruit &amp; Scharmer.

Title: Sunspot Structure and Dynamics
Authors: Weiss, N. O.
Bibcode: 2006SSRv..124...13W
Altcode: 2006SSRv..tmp...87W
  Sunspots are the most prominent magnetic features on the Sun but it
  is only within the last few years that the intricate structure of
  their magnetic fields has been resolved. In the penumbra the fields
  in bright and dark filaments differ in inclination by 30°. The field
  in the bright filaments is less inclined to the vertical, while the
  field in dark filaments becomes almost horizontal at the edge of the
  spot. Recent models suggest that this interlocking-comb structure is
  maintained through downward pumping of magnetic flux by small-scale
  granular convection, and that filamentation originates as a convective
  instability. Within the bright filaments convection patterns travel
  radially owing to the inclination of the field. A proper understanding
  of these processes requires new observations, from space and from the
  ground, coupled with large-scale numerical modelling.

Title: Hughes, Rosner, Weiss: Stellar MHD: Magnetohydrodynamics of
    stellar interiors
Authors: Hughes, David; Rosner, Robert; Weiss, Nigel
Bibcode: 2005A&G....46d..35H
Altcode:
  David Hughes, Robert Rosner and Nigel Weiss describe what was
  achieved during a programme on stellar magnetic fields at the Isaac
  Newton Institute in Cambridge. Over a four-month period more than
  90 participants visited the Institute for a mixture of structured
  workshops and informal collaboration.

Title: Linear and nonlinear dynamos
Authors: Weiss, N. O.
Bibcode: 2005AN....326..157W
Altcode:
  More than eighty years have passed since the idea of a solar dynamo was
  first put forward, and almost fifty years since Parker's pioneering
  paper. Yet dynamo theory remains a fertile subject and continues
  to raise new challenges, both physical and mathematical. So far,
  nearly all treatments have relied on mean field electrodynamics. The
  earliest models were linear but recent treatments have been nonlinear
  and increasingly sophisticated. During his career, Michael Stix has
  made major contributions to all branches of this subject. In this
  survey I shall review the historical development of dynamo theory, as
  applied to stars like the Sun, and then focus on some issues of current
  interest, ranging from axisymmetric calculations in spherical geometry
  to low-order models. Finally, I shall look ahead to what is needed in
  order to develop fully consistent, three-dimensional numerical models
  of the solar cycle.

Title: Book review of The magnetic universe, geophysical and
    astrophysical dynamo theory, by G. Rüdiger and R. Hollerbach,
    Wiley-VCH, Weinheim, 2004, XI+332 pp., £90.00, $161.00,
&amp;euro;135.00, hardback (ISBN: 3-527-40409-0).
Authors: Weiss, Nigel
Bibcode: 2005GApFD..99..347W
Altcode:
  No abstract at ADS

Title: Fluid Dynamics and Dynamos in Astrophysics and Geophysics:
    reviews emerging from the Durham Symposium on Astrophysical Fluid
    Mechanics held July 29 to August 8, 2002
Authors: Soward, Andrew M.; Jones, Christopher A.; Hughes, David W.;
   Weiss, Nigel O.
Bibcode: 2005fdda.conf.....S
Altcode:
  No abstract at ADS

Title: Solar and stellar physics - II
Authors: Weiss, N. O.
Bibcode: 2004Obs...124..348W
Altcode:
  No abstract at ADS

Title: Fine Structure in Sunspots
Authors: Thomas, John H.; Weiss, Nigel O.
Bibcode: 2004ARA&A..42..517T
Altcode:
  Important physical processes on the Sun, and especially in sunspots,
  occur on spatial scales at or below the limiting resolution of
  current solar telescopes. Over the past decade, using a number of
  new techniques, high-resolution observations have begun to reveal
  the complex thermal and magnetic structure of a sunspot, along with
  associated flows and oscillations. During this time remarkable advances
  in computing power have allowed significant progress in our theoretical
  understanding of the dynamical processes, such as magnetoconvection,
  taking place within a sunspot. In this review we summarize the latest
  observational results and theoretical interpretations of the fine
  structure in sunspots. A number of projects underway to build new solar
  telescopes or upgrade existing ones, along with several promising new
  theoretical ideas, ensure that there will be significant advances in
  sunspot research over the coming decade.

Title: Sunspots: The puzzling structure of a sunspot
Authors: Tobias, Steven; Weiss, Nigel
Bibcode: 2004A&G....45d..28T
Altcode:
  High-resolution observations of fine structure in sunspots have at
  last made it possible to answer a very old question: what causes the
  filamentary structure of the penumbra, with magnetic fields forming an
  interlocking comb-like configuration, that surrounds the dark central
  umbra of a sunspot? This unexpected geometry can only be explained
  by an understanding of the interaction between magnetic fields and
  small-scale turbulent convection outside the spot. This interaction
  leads to downwards transport of magnetic flux, submerging magnetic
  flux tubes below the solar surface and resulting in a strongly fluted
  structure. An idealized version of this process can be demonstrated
  in numerical experiments.

Title: On the origin of filamentary structure in sunspot penumbrae:
    non-linear results
Authors: Tildesley, M. J.; Weiss, N. O.
Bibcode: 2004MNRAS.350..657T
Altcode:
  As the magnetic flux in a pore increases, it grows in radius and the
  magnetic field at its outer edge becomes increasingly inclined to
  the vertical. It is believed that this increased field inclination
  causes filamentary convection to set in and that this new pattern
  of convection eventually develops into the highly fluted azimuthal
  structure of sunspots. The linear instability was investigated in a
  highly idealized Boussinesq model by Tildesley. A non-linear extension
  of this work is carried out here and the saturation of the instability
  is explored. These solutions are contrasted with those obtained when the
  upper-boundary condition is modified by matching the magnetic field to
  a potential field above the convecting layer. In the non-linear regime
  an alternating pattern of hot and cool stripes is produced at the
  upper surface. The results from these model calculations are related
  to the transition from pores to protospots and to the development of
  penumbral filaments in sunspots.

Title: Global Magnetorotational Instability with Inflow. I. Linear
    Theory and the Role of Boundary Conditions
Authors: Kersalé, Evy; Hughes, David W.; Ogilvie, Gordon I.; Tobias,
   Steven M.; Weiss, Nigel O.
Bibcode: 2004ApJ...602..892K
Altcode:
  We formulate a model system suitable for the systematic numerical
  investigation of global aspects of the magnetorotational instability
  and nonlinear dynamo action in accretion disks. The model consists
  of a cylindrical annulus occupied by an incompressible fluid with
  explicit viscosity and resistivity. Boundary conditions are imposed
  that permit an accretion flow appropriate to the stresses acting within
  the fluid to develop freely through the annulus. A steady basic state
  is identified in which a slow, steady accretion flow is driven by the
  explicit viscosity. We investigate the linear theory of this state
  subject to different choices of boundary conditions. The choice of
  boundary conditions is a crucial factor in determining the nature and
  growth rate of the instabilities. It is found that very rapidly growing
  wall modes occur generically, drawing energy artificially from outside
  the computational domain. However, by carefully selecting boundary
  conditions for which the total pressure is constrained at the radial
  boundaries, the wall modes are found to have growth rates bounded
  by the local properties of the magnetorotational instability. The
  resulting model provides the basis for a systematic exploration of
  nonlinear behavior in our future work.

Title: The Origin of Penumbral Structure in Sunspots: Downward
    Pumping of Magnetic Flux
Authors: Weiss, Nigel O.; Thomas, John H.; Brummell, Nicholas H.;
   Tobias, Steven M.
Bibcode: 2004ApJ...600.1073W
Altcode:
  This paper offers the first coherent picture of the interactions
  between convection and magnetic fields that lead to the formation of
  the complicated filamentary structure of a sunspot penumbra. Recent
  observations have revealed the intricate interlocking-comb structure
  of the penumbral magnetic field. Some field lines, with associated
  Evershed outflows, plunge below the solar surface near the edge of
  the spot. We claim that these field lines are pumped downward by
  small-scale granular convection outside the sunspot. This mechanism
  is demonstrated in numerical experiments. Magnetic pumping is a key
  new ingredient that links several theoretical ideas about penumbral
  structure and dynamics; it explains not only the abrupt appearance of
  a penumbra as a pore increases in size but also the behavior of moving
  magnetic features outside a spot.

Title: The Sun, An Introduction, by M. Stix, Astronomy and
    Astrophysics Library, Springer Berlin, Heidelberg, New York,
    Barcelona, Hong Kong, London, Milan, Paris, Tokyo, 2nd ed. 2002,
XVI+490 pp., EUR 79,95, hardback (ISBN: 3-540-42886-0)
Authors: Weiss, Nigel
Bibcode: 2003GApFD..97..421W
Altcode:
  Available from <A
  href="http://taylorandfrancis.metapress.com/openurl.asp?genre=article&amp;issn=0309-1929&amp;volume=97&amp;issue=5&amp;spage=421">http://taylorandfrancis.metapress.com/openurl.asp?genre=article&amp;issn=0309-1929&amp;volume=97&amp;issue=5&amp;spage=421</A>

Title: On the Interaction between Convection and Magnetic Fields
Authors: Cattaneo, Fausto; Emonet, Thierry; Weiss, Nigel
Bibcode: 2003ApJ...588.1183C
Altcode:
  Turbulent convection in the solar photosphere can act as a small-scale
  dynamo, maintaining a disordered magnetic field that is locally
  intense. On the other hand, convection is inhibited in the presence
  of a strong, externally imposed magnetic field, as for instance,
  in a sunspot. Large-scale, three-dimensional, numerical experiments
  on highly nonlinear magnetoconvection in a Boussinesq fluid show
  that there is a continuous transition from a dynamo regime through
  a convective regime to an oscillatory regime as the strength of the
  imposed magnetic field is progressively increased. The patterns found
  in these different regimes are described and analyzed.

Title: Modelling solar and stellar magnetoconvection
Authors: Weiss, Nigel
Bibcode: 2003safd.book..329W
Altcode:
  Numerical experiments on three-dimensional convection in the presence
  of an externally imposed magnetic field reveal a range of behaviour
  that can be compared with that observed at the surface of the Sun
  (and therefore expected to be present in other similar stars). In a
  strongly stratified compressible layer small-scale convection gives
  way to a regime with flux separation as the field strength is reduced;
  with a weak mean field magnetic flux is concentrated into narrow
  lanes enclosing vigorously convecting plumes. Small-scale dynamos,
  generating disordered magnetic fields, have been found in Boussinesq
  calculations with very high magnetic Reynolds numbers; there is a
  gradual transition from dynamo action to magnetoconvection as the
  strength of the imposed field is increased.

Title: Modelling Stellar Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 2003IAUS..210..127W
Altcode:
  No abstract at ADS

Title: Magnetic flux separation in photospheric convection
Authors: Weiss, N. O.; Proctor, M. R. E.; Brownjohn, D. P.
Bibcode: 2002MNRAS.337..293W
Altcode:
  Three-dimensional non-linear magnetoconvection in a strongly stratified
  compressible layer exhibits different patterns as the strength of
  the imposed magnetic field is reduced. There is a transition from a
  magnetically dominated regime, with small-scale convection in slender
  hexagonal cells, to a convectively dominated regime, with clusters of
  broad rising plumes that confine the magnetic flux to narrow lanes where
  fields are locally intense. Both patterns can coexist for intermediate
  field strengths, giving rise to flux separation: clumps of vigorously
  convecting plumes, from which magnetic flux has been excluded, are
  segregated from regions with strong fields and small-scale convection. A
  systematic numerical investigation of these different states shows
  that flux separation can occur over a significant parameter range and
  that there is also hysteresis. The results are related to the fine
  structure of magnetic fields in sunspots and in the quiet Sun.

Title: Downward pumping of magnetic flux as the cause of filamentary
    structures in sunspot penumbrae
Authors: Thomas, John H.; Weiss, Nigel O.; Tobias, Steven M.; Brummell,
   Nicholas H.
Bibcode: 2002Natur.420..390T
Altcode:
  The structure of a sunspot is determined by the local interaction
  between magnetic fields and convection near the Sun's surface. The dark
  central umbra is surrounded by a filamentary penumbra, whose complicated
  fine structure has only recently been revealed by high-resolution
  observations. The penumbral magnetic field has an intricate and
  unexpected interlocking-comb structure and some field lines, with
  associated outflows of gas, dive back down below the solar surface
  at the outer edge of the spot. These field lines might be expected
  to float quickly back to the surface because of magnetic buoyancy,
  but they remain submerged. Here we show that the field lines are kept
  submerged outside the spot by turbulent, compressible convection,
  which is dominated by strong, coherent, descending plumes. Moreover,
  this downward pumping of magnetic flux explains the origin of the
  interlocking-comb structure of the penumbral magnetic field, and the
  behaviour of other magnetic features near the sunspot.

Title: Umbral and penumbral magnetoconvection
Authors: Weiss, N. O.
Bibcode: 2002AN....323..371W
Altcode:
  Compressible convection in a strong vertical magnetic field can take two
  forms: either there is a regular pattern of small plumes or else the
  field separates from the motion giving regions of vigorous convection
  and regions that are magnetically dominated. In an inclined field,
  patterns are bound to travel. When the magnetic field is almost
  horizontal, convection takes the form of rolls aligned with the
  field. In the umbra of a sunspot convection will take the form of
  spatially modulated oscillations, giving rise to umbral dots. The
  penumbral field shows an interlocking-comb structure. In the bright
  filaments the magnetic field is inclined to the horizontal and modulated
  travelling waves, moving inwards or outwards, can give rise to the
  migration of bright grains. In the dark filaments the field is nearly
  horizontal, allowing only inefficient overturning convection.

Title: Magnetic flux pumping and the structure of a sunspot penumbra
Authors: Thomas, J. H.; Weiss, N. O.; Tobias, S. M.; Brummell, N. H.
Bibcode: 2002AN....323..383T
Altcode:
  We propose an overall scenario for the development and maintenance of
  a sunspot penumbra, in which turbulent magnetic flux pumping plays a
  key role. Recent high-resolution observations have revealed arched,
  "returning" magnetic flux tubes that emerge in the inner or middle
  penumbra, dive back down below the solar surface near the outer edge
  of the penumbra, and carry much of the Evershed flow. Some mechanism
  is required to keep the outer parts of the returning flux tubes
  submerged in spite of their magnetic buoyancy. We have proposed that
  the relevant mechanism is downward turbulent pumping of magnetic flux
  by granular convection in the moat outside the sunspot. This mechanism
  is demonstrated by means of an appropriate three-dimensional numerical
  simulation of turbulent compressible convection in the strongly
  superadiabatic granulation layer. We suggest that a penumbra first
  forms through a convectively driven instability at the outer edge
  of a growing pore. The nonlinear development of this instability
  pUSA)roduces the filamentary penumbra with its interlocking-comb
  magnetic field geometry. Downward flux pumping of some of the nearly
  horizontal magnetic flux in the dark filaments produces the returning
  flux tubes, with their associated Evershed flow, and also establishes
  the subcritical nature of the bifurcation that produces the filamentary
  penumbra, which explains why there are pores larger than the smallest
  sunspots.

Title: Presidential Address: Dynamos in planets, stars and galaxies
Authors: Weiss, Nigel
Bibcode: 2002A&G....43c...9W
Altcode:
  Nigel Weiss discusses dynamos in settings as diverse as galaxies and
  planets in this his 2000 Presidential Address to the Ordinary (A&amp;G)
  Meeting of the Royal Astronomical Society. &lt;heading id="h10"
  level="1"&lt;/heading&gt; <P />Global magnetic fields in the Earth
  and other major planets, in the Sun and other active stars, and also
  in spiral galaxies like the Milky Way, are apparently maintained by
  hydromagnetic dynamos. This lecture will contrast the various dynamo
  models that have been put forward. Powerful supercomputers have now
  made it possible to simulate the geodynamo in considerable detail. In
  the case of the Sun, we have yet to explain its internal rotation
  and models still have to rely on mean field dynamo theory. There are
  many features that can be explained but extrapolation to other stars
  remains uncertain. For galaxies, even the need for a dynamo is still
  controversial.

Title: On the Origin of the Solar Mesogranulation
Authors: Cattaneo, Fausto; Lenz, Dawn; Weiss, Nigel
Bibcode: 2001ApJ...563L..91C
Altcode:
  The observed properties of mesogranules are related to structures found
  in idealized numerical experiments on turbulent convection. We describe
  results obtained for three-dimensional Boussinesq convection in a layer
  with a very large aspect ratio. There are two distinct cellular patterns
  at the surface. Energy-transporting convection cells (corresponding
  to granules in the solar photosphere) have diameters comparable to
  the layer depth, while macrocells (corresponding to mesogranules)
  are several times larger. The motion acts as a small-scale turbulent
  dynamo, generating a disordered magnetic field that is concentrated
  at macrocellular corners and, to a lesser extent, in the lanes that
  join them. These results imply that mesogranules owe their origin to
  collective interactions between the granules.

Title: Sustaining the Sun's Magnetic Network with Emerging Bipoles
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 2001ApJ...561..427S
Altcode:
  The Michelson Doppler Imager experiment on SOHO has revealed a
  ``magnetic carpet'' dominated by the emergence of bipolar magnetic flux
  in ephemeral active regions, which subsequently split into small flux
  elements that drift into the magnetic network. The effects of granular
  and supergranular convection on these flux elements are represented
  here by kinematic modeling: Elementary flux tubes are transported
  passively by the supergranular flow, while experiencing small random
  displacements produced by granulation. They end up in the magnetic
  network that surrounds the supergranules, where they eventually meet
  oppositely directed fields and are annihilated. The model calculations
  show that the total unsigned magnetic flux will decay within a few
  days unless it is continually replenished. A statistically steady
  state with a total unsigned flux of 2-3×10<SUP>23</SUP> Mx over the
  whole solar surface can be maintained if bipolar flux emerges at a rate
  of 7×10<SUP>22</SUP> Mx day<SUP>-1</SUP>, as indicated by published
  measurements of the rate at which ephemeral active regions appear.

Title: Presidential Address: Turbulent magnetic fields in the Sun
Authors: Weiss, Nigel
Bibcode: 2001A&G....42c..10W
Altcode:
  Nigel Weiss recounts his Presidential Address 2001, given to the RAS
  A&amp;G Ordinary Meeting on 9 February 2001. <P />Recent high-resolution
  observations, from the ground and from space, have revealed the fine
  structure of magnetic features at the surface of the Sun. At the same
  time, advances in computing power have at last made it possible to
  develop models of turbulent magnetoconvection that can be related to
  these observations. The key features of flux emergence and annihilation,
  as observed by the MDI experiment on SOHO, are reproduced in kinematic
  calculations, while three-dimensional numerical experiments reveal the
  dynamical processes that are involved. The pattern of convection depends
  on the strength of the magnetic field: as the mean field decreases,
  slender rising plumes give way to a regime where magnetic flux is
  separated from the motion and then to one where locally intense magnetic
  fields nestle between broad and vigorously convecting plumes. Moreover,
  turbulent convection is itself able to act as a small-scale dynamo,
  generating disordered fields near the solar surface.

Title: How the Sun Maintains its Magnetic Network
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 2001AAS...198.8601S
Altcode: 2001BAAS...33..913S
  The MDI experiment on SOHO has revealed a `magnetic carpet' dominated
  by the emergence of bipolar magnetic flux in ephemeral active regions,
  which subsequently split into small flux elements that drift into the
  magnetic network. The effects of granular and supergranular convection
  on these flux elements are represented here by kinematic modeling:
  Elementary flux tubes are transported passively by the supergranular
  flow, while experiencing small random displacements produced by
  granulation. They end up in the magnetic network that surrounds the
  supergranules, where they eventually meet oppositely directed fields and
  are annihilated. The model calculations show that the total unsigned
  magnetic flux will decay within a few days unless it is continually
  replenished. A statistically steady state with a total unsigned
  flux of 2-3 x 10<SUP>23</SUP> Mx over the whole solar surface can be
  maintained if bipolar flux emerges at a rate of 7 x 10<SUP>22</SUP>
  Mx d<SUP>-1</SUP>, as indicated by published measurements of the rate
  at which ephemeral active regions appear.

Title: Flux Separation in Photospheric Magnetoconvection
Authors: Weiss, N. O.; Proctor, M. R. E.
Bibcode: 2001IAUS..203..219W
Altcode:
  Numerical experiments on three-dimensional magnetoconvection in a
  stratified compressible layer yield results that can now be compared
  with the high resolution observations of granulation and intergranular
  magnetic fields obtained at La Palma, and related to the slender
  loops revealed by TRACE. As the imposed magnetic field strength
  is decreased there is a transition from small-scale plumes, in the
  magnetically dominated regime, to large-scale vigorous plumes when the
  field is dominated by the motion. In the intermediate regime magnetic
  flux separates from the motion, so that there are almost field-free
  regions, with clusters of vigorous plumes, surrounded by regions where
  the Lorentz force is strong enough to control the dynamics. There
  is a range of field strengths where either small-scale plumes or
  flux-separated solutions can persist, depending on initial conditions
  for the computation. The patterns revealed in these calculations can
  be related to convection in sunspot umbrae (where there is a strong
  vertical field, and the appearance of umbral dots, to the formation
  of plage regions and to the behaviour of intergranular fields in the
  quiet Sun. In the weak field limit, turbulent convection is able to
  act as a dynamo and to maintain a disordered field.

Title: Generation of Coronal Currents by the Solar Convection Zone
Authors: Galloway, D. J.; Uchida, Y.; Weiss, N. O.
Bibcode: 2001PASA...18..329G
Altcode:
  : Solar flares are thought to be caused by reconnection of magnetic
  fields and their associated electric currents in the solar corona. The
  currents have to be there to provide available energy over and above
  the current-free minimum energy state, but what generates them has been
  little discussed. This paper investigates the idea that twisting motions
  in the turbulent convection zone below may provide a natural source for
  the currents and explain some of their properties. The twists generate
  upward-propagating Alfvén waves with a Poynting flux of the right order
  of magnitude to power a flare. Depending on the depth it takes place,
  the twisting event that initiates a particular flare may occur hours,
  days or even months before the flare itself.

Title: Physical Causes of Solar Activity
Authors: Weiss, N. O.; Tobias, S. M.
Bibcode: 2000SSRv...94...99W
Altcode:
  The magnetic fields that dominate the structure of the Sun's atmosphere
  are controlled by processes in the solar interior, which cannot be
  directly observed. Magnetic activity is found in all stars with deep
  convective envelopes: young and rapidly rotating stars are very active
  but cyclic activity only appears in slow rotators. The Sun's 11-year
  activity cycle corresponds to a 22-year magnetic cycle, since the
  sunspot fields (which are antisymmetric about the equator) reverse
  at each minimum. The record of magnetic activity is aperiodic and
  is interrupted by episodes of reduced activity, such as the Maunder
  Minimum in the seventeenth century, when sunspots almost completely
  disappeared. The proxy record from cosmogenic isotopes shows that
  similar grand minima recur at intervals of around 200 yr. The Sun's
  large-scale field is generated by dynamo action rather than by an
  oscillator. Systematic magnetic cycles are apparently produced by a
  dynamo located in a region of weak convective overshoot at the base
  of the convection zone, where there are strong radial gradients in
  the angular velocity Ω. The crucial parameter (the dynamo number)
  increases with increasing Ω and kinematic (linear) theory shows that
  dynamo action can set in at an oscillatory (Hopf) bifurcation that is
  probably subcritical. Although it has been demonstrated that the whole
  process works in a self-consistent model, most calculations have relied
  on mean-field dynamo theory. This approach is physically plausible
  but can only be justified under conditions that do not apply in the
  Sun. Still, mean-field dynamos do reproduce the butterfly diagram and
  other key features of the solar cycle. An alternative approach is to
  study generic behaviour in low-order models, which exhibit two forms
  of modulation, associated with symmetry-breaking and with reduced
  activity. Comparison with observed behaviour suggests that modulation
  of the solar cycle is indeed chaotic, i.e. deterministically rather
  than stochastically driven.

Title: Sunspots
Authors: Weiss, N.
Bibcode: 2000eaa..bookE2050W
Altcode:
  Sunspots are the sites of strong magnetic fields at the surface
  of the Sun. They are visible as features that appear dark because
  they are cooler than the surrounding SOLAR PHOTOSPHERE, owing to
  partial suppression of convective energy transport by the magnetic
  field. Sunspots are distinguished from SUNSPOT PORES by having a
  filamentary SUNSPOT PENUMBRA surrounding a dark SUNSPOT UMBRA. Their
  dia...

Title: Resonance in a coupled solar-climate model
Authors: Tobias, S. M.; Weiss, N. O.
Bibcode: 2000SSRv...94..153T
Altcode:
  The 11-year solar activity cycle is magnetic in origin and is
  responsible for small changes in solar luminosity and the modulation
  of the solar wind. The terrestrial climate exhibits much internal
  variability supporting oscillations with many frequencies. The direct
  effect of changing solar irradiance in driving climatic change is
  believed to be small, and amplification mechanisms are needed to
  enhance the role of solar variability. In this paper we demonstrate
  that resonance may play a crucial role in the dynamics of the climate
  system, by using the output from a nonlinear solar dynamo model as a
  weak input to a simplified climate model. The climate is modelled as
  oscillating about two fixed points (corresponding to a warm and cold
  state) with the weak chaotically modulated solar forcing on average
  pushing the solution towards the warm state. When a typical frequency
  of the input is similar to that of the chaotic climate system then
  a dramatic increase in the role of the solar forcing is apparent and
  complicated intermittent behaviour is observed. The nonlinear effects
  are subtle however, and forcing that on average pushes the solution
  towards the warm state may lead to increased intervals of oscillation
  about either state. Owing to the intermittent nature of the timeseries,
  analysis of the relevant timeseries is shown to be non-trivial.

Title: Turbulent Convection, Rotation, and the Solar Dynamo
Authors: Tobias, Steve; Toomre, Juri; Weiss, Nigel
Bibcode: 2000astu.progE..30T
Altcode:
  No abstract at ADS

Title: The Influence of Internal Heating on Nonlinear Compressible
    Convection
Authors: Hurlburt, N. E.; Weiss, N. O.
Bibcode: 2000SPD....31.0506H
Altcode: 2000BAAS...32..837H
  In the bulk of the solar convection zone we expect convection to be
  efficient and therefore maintain an adiabatic temperature gradient. In
  most numerical simulations of solar convection the total energy flux
  within this region is due to the conduction down this gradient (which is
  small) and the various contributions due to the convective motions. What
  has often been neglected is the contribution that is transported by
  radiation. The contribution of this flux decreases across the layer
  and thereby deposits a significant amount of thermal energy in the
  midst of the convection zone. This is in contrast to most simulations
  of the convection where the input of energy is supplied exclusively
  by conduction from the boundaries. Mixing length models predict that
  approximately half of the total energy input to the solar convection
  zone is deposited, more-or-less uniformly over the convection zone, with
  the remaining half being conducted from the lower boundary. Thus the
  study of the behavior of internally-heated compressible convection is
  warranted. Previous studies of internally heated compressible convection
  have been inconclusive due to the shearing instabilities that arise
  in simple, periodic domains. Here we suppress these instabilities by
  considering flows in axisymmetric geometries. We conduct surveys of
  the structure and dynamics of the resulting flows and present possible
  applications to observed solar and stellar phenomena.

Title: Resonance in a Coupled Solar-Climate Model
Authors: Tobias, S. M.; Weiss, N. O.
Bibcode: 2000svc..book..153T
Altcode:
  No abstract at ADS

Title: Physical Causes of Solar Activity
Authors: Weiss, N. O.; Tobias, S. M.
Bibcode: 2000svc..book...99W
Altcode:
  No abstract at ADS

Title: Symmetry Considerations in Stellar Dynamos
Authors: Tobias, S. M.; Knobloch, E.; Weiss, N. O.
Bibcode: 1999ASPC..178..185T
Altcode: 1999sdnc.conf..185T
  No abstract at ADS

Title: Modelling photospheric magnetoconvection
Authors: Blanchflower, S. M.; Rucklidge, A. M.; Weiss, N. O.
Bibcode: 1998MNRAS.301..593B
Altcode:
  The increasing power of computers makes it possible to model the
  non-linear interaction between magnetic fields and convection at
  the surfaces of solar-type stars in ever greater detail. We present
  the results of idealized numerical experiments on two-dimensional
  magnetoconvection in a fully compressible perfect gas. We first vary
  the aspect ratio lambda of the computational box and show that the
  system runs through a sequence of convective patterns, and that it is
  only for a sufficiently wide box (lambda&gt;=6) that the flow becomes
  insensitive to further increases in lambda. Next, setting lambda=6,
  we decrease the field strength from a value strong enough to halt
  convection and find transitions to small-scale steady convection, next
  to spatially modulated oscillations (first periodic, then chaotic)
  and then to a new regime of flux separation, with regions of strong
  field (where convection is almost completely suppressed) separated
  by broad convective plumes. We also explore the effects of altering
  the boundary conditions and show that this sequence of transitions
  is robust. Finally, we relate these model calculations to recent
  high-resolution observations of solar magnetoconvection, in plage
  regions as well as in light bridges and the umbrae of sunspots.

Title: Flux expulsion by inhomogeneous turbulence
Authors: Tao, L.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1998MNRAS.300..907T
Altcode:
  Flux expulsion is an important consequence of the interaction of
  magnetic fields with fluid convection and has been well studied for
  particular cases of steady, single-cell flows. Here we examine a
  related phenomenon in inhomogeneous turbulence using direct numerical
  simulations. To understand our numerical results, we analyse average
  properties of our model, and obtain mean transport coefficients
  which can be used to describe the approach of the system to its final
  state. For the kinematic problem these transport coefficients give an
  excellent prediction of the expulsion process; however, the enhanced
  transport is suppressed by dynamical back-reaction of the Lorentz
  force. Finally, we discuss the astrophysical implications for magnetic
  fields in stellar convection zones. Segregation of magnetic fields from
  turbulent motion not only allows strong toroidal fields to accumulate
  in regions of convective overshoot but also permits significant poloidal
  fields to be maintained by dynamo action in stars like the Sun.

Title: Modulation and symmetry changes in stellar dynamos
Authors: Knobloch, E.; Tobias, S. M.; Weiss, N. O.
Bibcode: 1998MNRAS.297.1123K
Altcode:
  Stellar dynamos are governed by non-linear partial differential
  equations (PDEs) which admit solutions with dipole, quadrupole or mixed
  symmetry (i.e. with different parities). These PDEs possess periodic
  solutions that describe magnetic cycles, and numerical studies reveal
  two different types of modulation. For modulations of Type 1 there
  are parity changes without significant changes of amplitude, while
  for Type 2 there are amplitude changes without significant changes in
  parity. In stars like the Sun, cyclic magnetic activity is interrupted
  by grand minima that correspond to Type 2 modulation. Although the
  Sun's magnetic field has maintained dipole symmetry for almost 300
  yr, there was a significant parity change at the end of the Maunder
  Minimum. We infer that the solar field may have flipped from dipole
  to quadrupole polarity (and back) after deep minima in the past and
  may do so again in the future. Other stars, with different masses or
  rotation rates, may exhibit cyclic activity with dipole, quadrupole
  or mixed parity. The origins of such behaviour can be understood
  by relating the PDE results to solutions of appropriate low-order
  systems of ordinary differential equations (ODEs). Type 1 modulation
  is reproduced in a fourth-order system while Type 2 modulation occurs
  in a third-order system. Here we construct a new sixth-order system
  that describes both types of modulation and clarifies the interactions
  between symmetry-breaking and modulation of activity. Solutions of these
  non-linear ODEs reproduce the qualitative behaviour found for the PDEs,
  including flipping of polarity after a prolonged grand minimum. Thus
  we can be confident that these patterns of behaviour are robust,
  and will apply to stars that are similar to the Sun.

Title: An Active Sun Throughout the Maunder Minimum
Authors: Beer, Jürg; Tobias, Steven; Weiss, Nigel
Bibcode: 1998SoPh..181..237B
Altcode:
  Measurements of <SUP>10</SUP>Be concentration in the Dye 3 ice core
  show that magnetic cycles persisted throughout the Maunder Minimum,
  although the Sun's overall activity was drastically reduced and sunspots
  virtually disappeared. Thus the dates of maxima and minima can now be
  reliably estimated. Similar behaviour is shown by a nonlinear dynamo
  model, which predicts that, after a grand minimum, the Sun's toroidal
  field may switch from being antisymmetric to being symmetric about the
  equator. The presence of cyclic activity during the Maunder Minimum
  limits estimates of the solar contribution to climatic change.

Title: Flux Separation in Stellar Magnetoconvection
Authors: Tao, L.; Weiss, N. O.; Brownjohn, D. P.; Proctor, M. R. E.
Bibcode: 1998ApJ...496L..39T
Altcode:
  The effect of a strong magnetic field on photospheric convection in a
  cool star like the Sun can be established by relating high-resolution
  solar observations to results from nonlinear models that rely on
  computation. The patterns of motion in numerical experiments on
  three-dimensional, compressible magnetoconvection depend not only on
  the strength of the imposed vertical magnetic field but also on the
  aspect ratio λ of the computational box. In a wide box (λ=8) with a
  moderately strong field, the flow organizes itself so that magnetic flux
  is separated from the motion. There are regions with strong fields and
  small-scale oscillatory convection next to almost field-free regions
  with clusters of broad and vigorous convective plumes. In the solar
  photosphere, this corresponds to the difference between the patterns
  of granulation in plage regions (with fields greater than 100 G)
  and in the adjacent quiet Sun.

Title: Kinematic Modeling of Vortices in the Solar Photosphere
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1997ApJ...489..960S
Altcode:
  The application of local correlation tracking to the proper motions of
  granules yields the horizontal velocity field at the solar surface. The
  divergence of the velocity reveals a pattern of sources and sinks. The
  vorticity is concentrated at sinks to form local swirls (with either
  sense of motion). A simple kinematic model of such a vortex, in
  which the radial inflow is balanced by an eddy viscosity, predicts
  that the vorticity should have a Gaussian profile. This prediction is
  confirmed by comparison with three sets of high-resolution observations,
  obtained from Spacelab 2 and from the Swedish Vacuum Solar Telescope
  on La Palma. Finally, we develop a more precise version of the model
  and provide an estimate of the eddy viscosity due to small-scale
  granulation.

Title: Physics of the solar dynamo
Authors: Weiss, N. O.
Bibcode: 1997ppvs.conf..325W
Altcode:
  Introduction Stellar magnetic cycles Solar magnetic activity Stellar
  activity Origins of the Sun's magnetic field Dynamo theory The
  kinematic dynamo problem Nonlinear equilibration Mean-field dynamo
  theory Modulation of activity cycles Toy models Global models Solar
  activity and climatic change Observational correlations Mechanisms
  and speculations

Title: Modulation of Solar and Stellar Activity Cycles
Authors: Weiss, N. O.; Tobias, S. M.
Bibcode: 1997LNP...489...25W
Altcode: 1997shpp.conf...25W
  Cyclic magnetic activity in the Sun and other similar stars is
  interrupted by episodes of reduced activity such as the Maunder
  Minimum. This pattern is reproduced in mean field (αθ) dynamo models,
  where growth of the field is limited by the nonlinear action of the
  Lorentz force on differential rotation. The observed aperiodicity
  can be ascribed to deterministic rather than stochastic processes,
  and chaotic modulation is demonstrated for a low-order system, for
  two-dimensional dynamo waves and for a simple global model. Amplitude
  modulation that leads to grand minima is distinct from modulation
  associated with changes in the symmetry of the field.

Title: Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 1997ASPC..118...21W
Altcode: 1997fasp.conf...21W
  Two recent computational treatments of the nonlinear interaction
  between convection and magnetic fields are described and contrasted. The
  first is a sequence of numerical experiments on an idealized model of
  three-dimensional compressible magnetoconvection, with an emphasis
  on changes in the magnetic field structure and the velocity pattern
  as the strength of the imposed field is reduced. The second is a
  two-dimensional simulation of the formation and evolution of a highly
  dynamical magnetic flux sheet, in a realistic model of the solar
  photosphere. The results are related to high-resolution observations
  of fine structure in sunspots and to the behaviour of intergranular
  magnetic fields.

Title: Photospheric Convection in Strong Magnetic Fields
Authors: Weiss, N. O.; Brownjohn, D. P.; Matthews, P. C.; Proctor,
   M. R. E.
Bibcode: 1996MNRAS.283.1153W
Altcode:
  The effect of magnetic fields on convection at the surfaces of
  cool stars can be explored by comparing the results of detailed
  numerical experiments with high-resolution solar observations. We
  have investigated non-linear three-dimensional magnetoconvection in
  a fully compressible perfect gas. In this paper we study the effect
  of an imposed magnetic field on the pattern of convection in a deep
  stratified layer. When the field is strong enough to dominate the
  motion we find steady convection with rising plumes on a deformed
  hexagonal lattice, and a magnetic network at the upper boundary. This
  gives way to spatially modulated oscillations for weaker fields. As the
  field strength is further reduced the oscillations become more violent
  and irregular, and their horizontal scale increases. Magnetic flux
  moves rapidly along the network that encloses the ephemeral plumes;
  when the imposed field is relatively weak, intense fields appear at
  junctions in the network, where the magnetic pressure is comparable to
  the gas pressure and an order of magnitude greater than the dynamic
  pressure. This behaviour is related to convection in sunspots and
  plages and to the structure of intergranular magnetic fields on the Sun.

Title: Dynamos in Different Types of Stars
Authors: Weiss, N. O.
Bibcode: 1996mpsa.conf..387W
Altcode: 1996IAUCo.153..387W
  No abstract at ADS

Title: Double-diffusive convection with two stabilizing gradients:
    strange consequences of magnetic buoyancy.
Authors: Hughes, D. W.; Weiss, N. O.
Bibcode: 1995JFM...301..383H
Altcode:
  Instabilities due to a vertically stratified horizontal magnetic field
  (magnetic buoyancy instabilities) are believed to play a key role in the
  escape of the Sun's internal magnetic field and the formation of active
  regions and sunspots. In a star the magnetic diffusivity is much smaller
  than the thermal diffusivity and magnetic buoyancy instabilities are
  double-diffusive in character. The authors have studied the nonlinear
  development of these instabilities, in an idealized two-dimensional
  model, by exploiting a non-trivial transformation between the governing
  equations of magnetic buoyancy and those of classical thermosolutal
  convection. The main result is extremely surprising. They have
  demonstrated the existence of finite-amplitude steady convection
  when both the influential gradients (magnetic and convective) are
  stabilizing. This strange behaviour is caused by the appearance of
  narrow magnetic boundary layers, which distort the mean pressure
  gradient so as to produce a convectively unstable stratification.

Title: Chaotically modulated stellar dynamos
Authors: Tobias, S. M.; Weiss, N. O.; Kirk, V.
Bibcode: 1995MNRAS.273.1150T
Altcode:
  Slowly rotating, late-type stars show intermittent cyclic magnetic
  activity, interrupted by grand minima. The record of the solar cycle
  is apparently chaotic. We construct a simple third-order model of a
  stellar dynamo following two different procedures. The first uses simple
  physical arguments based on the processes that occur in a dynamo. The
  second relies on bifurcation theory, with no explicit reference to the
  dynamo equations, and displays the essential mathematical structure
  of the model. Modulation of the basic cycle and chaos are found to be
  a natural consequence of the transition from a non-magnetic state to
  one with periodically reversing fields. The model is related to more
  general normal forms and it is shown that the behaviour described is
  generic and therefore robust.

Title: Kinematic Models of Supergranular Diffusion on the Sun
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 1995ApJ...442..886S
Altcode:
  We develop kinematic models of diffusion generated by supergranulation
  at the solar surface. These models use current observations for the
  size, horizontal velocity, and lifetime of supergranules. Because there
  is no observational description of the appearance and disappearance of
  supergranules, we investigate models using several plausible evolution
  processes, including the effect of different lifetime distribution
  functions for the cells. The results are quite insensitive to the
  methods chosen to replace old supergranules, the distribution of cell
  lifetimes, and even the cell lifetime itself, for mean lifetimes between
  15 to 30 hr. Calculated diffusion coefficients range between 500 and 700
  sq km/s, in agreement with the best fit diffusion coefficients used by
  Sheeley and his collaborators to model the large-scale distribution
  of magnetic fields over the solar surface. However, our models do
  not explain the field distribution in plage, and they predict that
  virtually all the strong field in quiet Sun exists in relatively
  isolated clumps. We suggest possible mechanisms for the creation of
  plage and the bright network seen in quiet Sun.

Title: The Structure of Sunspots
Authors: Weiss, N. O.
Bibcode: 1995SPD....26..301W
Altcode: 1995BAAS...27..952W
  No abstract at ADS

Title: The abrupt development of penumbrae in sunspots
Authors: Rucklidge, A. M.; Schmidt, H. U.; Weiss, N. O.
Bibcode: 1995MNRAS.273..491R
Altcode:
  A sunspot is distinguished from a pore by having a filamentary penumbra,
  corresponding to convective motions that carry energy into the spot
  from the surrounding field-free plasma. A simplified model of energy
  transport in sunspots is developed in order to model the transition
  from pores to spots as the magnetic flux is varied. The observed
  overlap between the radii of large pores and small spots implies that
  the filamentary convective mode sets in suddenly and rapidly, as in
  the idealized case where pore solutions lose stability at a bifurcation.

Title: Kinematic modelling of magnetoconvection
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.; Ginet, G. P.
Bibcode: 1994smf..conf..276S
Altcode:
  No abstract at ADS

Title: Solar and Stellar Dynamos
Authors: Weiss, N. O.
Bibcode: 1994lspd.conf...59W
Altcode:
  No abstract at ADS

Title: Modeling Solar Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 1994ASPC...68...45W
Altcode: 1994sare.conf...45W
  No abstract at ADS

Title: Magnetoconvective patterns
Authors: Weiss, N. O.
Bibcode: 1994ASIC..433..287W
Altcode:
  No abstract at ADS

Title: Kinematic Modeling of Magnetic Field Diffusion at the Solar
    Surface
Authors: Title, Alan M.; Simon, George W.; Weiss, Nigel O.
Bibcode: 1994ASPC...68...87T
Altcode: 1994sare.conf...87T
  No abstract at ADS

Title: Nonlinear three-dimensional magnetoconvection in a compressible
    atmosphere
Authors: Matthews, P. C.; Proctor, M. R. E.; Rucklidge, A. M.; Weiss,
   N. O.
Bibcode: 1994smf..conf..279M
Altcode:
  No abstract at ADS

Title: Nonlinear stellar dynamos.
Authors: Tobias, S. M.; Weiss, N. O.
Bibcode: 1994cmcp.conf...46T
Altcode:
  Slowly rotating late-type stars show intermittent cyclic activity,
  interrupted by grand minima. A simple third-order dynamo model
  describes the transition from a non-magnetic state to one with
  periodically reversing fields. As the rate of rotation is increased,
  subsequent bifurcations lead to periodically modulated cycles and then
  to chaotically modulated oscillations.

Title: Diffusion of "Corks" Over the Solar Surface
Authors: Title, A. M.; Simon, G. W.; Weiss, N. O.
Bibcode: 1993BAAS...25Q1183T
Altcode:
  No abstract at ADS

Title: Book-Review - Sunspots - Theory and Observations
Authors: Thomas, J. H.; Weiss, N. O.; Parkinson, J. H.
Bibcode: 1993Obs...113..145T
Altcode:
  No abstract at ADS

Title: Diffusion of ``Corks'' Over the Solar Surface
Authors: Title, A. M.; Simon, G. W.; Weiss, N. O.
Bibcode: 1993AAS...182.4804T
Altcode: 1993BAAS...25Q.880T
  Test particles in flow fields generated by correlation tracking of
  movies of the solar surface and kinematic models of the solar surface
  quickly collect in stagnation points of the flow fields and remain
  there. Test particles do not form a quasi-stable network pattern. The
  diffusion coefficients generated from a net of kinematic models with a
  range of cell sizes and lifetimes are not proportional to the cell size
  squared divided by the cell lifetime as commonally assumed. Reasonable
  estimates of cell sizes and lifetimes yield diffusiion coefficients that
  are lower than the 600 km(2) /s used by Sheeley and his collaborators in
  their surface diffusion models. We conclude that: 1) The appearance of
  plages and enhanced network can not be explained by adjustment of the
  cell sizes or surface velocities; and 2) diffusion is not sufficient
  to explain the appearance of plages and enhanced network.

Title: Magnetic geometry of sunspots
Authors: Weiss, Nigel
Bibcode: 1993Natur.362..208W
Altcode:
  No abstract at ADS

Title: Solar and Stellar Dynamos
Authors: Weiss, N. O.
Bibcode: 1993ASSL..183..541W
Altcode: 1993pssc.symp..541W
  No abstract at ADS

Title: Oscillations and secondary bifurcations in nonlinear
    magnetoconvection
Authors: Rucklidge, A. M.; Weiss, N. O.; Brownjohn, D. P.; Proctor,
   M. R. E.
Bibcode: 1993GApFD..68..133R
Altcode:
  Complicated bifurcation structures that appear in nonlinear
  systems governed by partial differential equations (PDEs) can be
  explained by studying appropriate low-order amplitude equations. We
  demonstrate the power of this approach by considering compressible
  magnetoconvection. Numerical experiments reveal a transition from a
  regime with a subcritical Hopf bifurcation from the static solution,
  to one where finite-amplitude oscillations persist although there
  is no Hopf bifurcation from the static solution. This transition is
  associated with a codimension-two bifurcation with a pair of zero
  eigenvalues. We show that the bifurcation pattern found for the
  PDEs is indeed predicted by the second-order normal form equation
  (with cubic nonlinearities) for a Takens - Bogdanov bifurcation
  with Z2 symmetry. We then extend this equation by adding quintic
  nonlinearities and analyse the resulting system. Its predictions provide
  a qualitatively accurate description of solutions of the full PDEs
  over a wider range of parameter values. Replacing the reflecting (Z2)
  lateral boundary conditions with periodic [O(2)] boundaries allows
  stable travelling wave and modulated wave solutions to appear; they
  could be described by a third-order system.

Title: Bifurcations and Symmetry-Breaking in Simple Models of
    Nonlinear Dynamos
Authors: Weiss, N. O.
Bibcode: 1993IAUS..157..219W
Altcode:
  No abstract at ADS

Title: Symmetries of time-dependent magnetoconvection
Authors: Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1993GApFD..70..137P
Altcode:
  In the presence of a magnetic field, convection may set in at a
  stationary or an oscillatory bifurcation, giving rise to branches
  of steady, standing wave and travelling wave solutions. Numerical
  experiments provide examples of nonlinear solutions with a variety
  of different spatiotemporal symmetries, which can be classified by
  establishing an appropriate group structure. For the idealized problem
  of two-dimensional convection in a stratified layer the system has
  left-right spatial symmetry and a continuous symmetry with respect
  to translations in time. For solutions of period P the latter can be
  reduced to Z2 symmetry by sampling solutions at intervals of ½P. Then
  the fundamental steady solution has the spatiotemporal symmetry D2 = Z2
  Z2 and symmetry-breaking yields solutions with Z2 symmetry corresponding
  to travelling waves, standing waves and pulsating waves. A further
  loss of symmetry leads to modulated waves. Interactions between the
  fundamental and its first harmonic are described by the group D2h =
  D2 ⊗ Z2 and its invariant subgroups, which describe solutions that
  are either steady or periodic in a uniformly moving frame. For a
  Boussinesq fluid in a layer with identical top and bottom boundary
  conditions there is also an up-down symmetry. With fixed lateral
  boundaries the spatiotemporal symmetries, again described by D2h
  and its invariant subgroups, can be related to results obtained in
  numerical experiments and analysed by Nagata et al. (1990). With
  periodic boundary conditions, the full symmetry group, D2h⊗Z2,
  is of order 16. Its invariant subgroups describe pure and mixed-mode
  solutions, which may be steady states, standing waves, travelling waves,
  pulsating waves or modulated waves.

Title: X-Ray Observations of Sunspot Penumbral Structure
Authors: Sams, B. J., III; Golub, L.; Weiss, N. O.
Bibcode: 1992ApJ...399..313S
Altcode:
  High-resolution coronal observations with the Normal Incidence X-ray
  Telescope (NIXT) reveal previously unobserved structure in the magnetic
  fields above a sunspot. The X-ray images are precisely aligned with
  a continuum photospheric image taken at the same time. The X-ray
  brightness traces magnetic field lines and shows: (1) that none of
  the bright loops originate in the spot umbra and (2) that some field
  lines emerging from the inner penumbra connect to regions far away
  from the spot. Such large-scale structures must remain distinct from
  the shallowly inclined fields in the outer penumbra. In particular,
  they cannot be involved in any interchange between the bright and dark
  filaments. This imposes constraints on models of penumbral convection.

Title: Kinematic Modeling of Active Region Decay
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 1992AAS...180.1101S
Altcode: 1992BAAS...24..746S
  No abstract at ADS

Title: Convective motion on the Sun
Authors: Weiss, Nigel
Bibcode: 1992Natur.356..287W
Altcode:
  No abstract at ADS

Title: The Theory of Sunspots
Authors: Thomas, John H.; Weiss, Nigel O.
Bibcode: 1992ASIC..375....3T
Altcode: 1992sto..work....3T
  This review covers the present state of our theoretical understanding
  of the physics of sunspots, along with the principal observational
  results that need to be explained. The topics covered range from the
  detailed structure of an individual sunspot to the broad connection
  between sunspots and the global solar magnetic field and the solar
  cycle. Our aim is to give a critical discussion of the theoretical ideas
  and models without presenting mathematical details. After outlining
  the historical development of the basic concepts associated with the
  magnetohydrodynamic theory of sunspots, we discuss recent treatments of
  their properties and structure, placing special emphasis on developments
  that have occurred within the last ten years. There have been remarkable
  improvements in the theoretical modelling of sunspots, led by new
  ideas and by more elaborate and realistic numerical simulations. At
  the same time, new observations have raised new theoretical questions
  or caused old ones to be reconsidered. In particular, measurements
  of oscillations in and around sunspots have opened up the new field
  of sunspot seismology, while recent high-resolution observations have
  forced us to rethink the structure of a sunspot penumbra.

Title: Sunspots - Theory &amp; Observations: NATO Cambridge, 1992
Authors: Thomas, John H.; Weiss, Nigel O.
Bibcode: 1992ASIC..375.....T
Altcode: 1992sto..work.....T
  The papers contained in this volume focus on theoretical problems
  associated with sunspots and present results of recent high-resolution
  observations of sunspots. In particular, attention is given to the
  evolution of sunspots, overall structure and fine structure of sunspots,
  waves and oscillations in sunspots, and the relation of sunspots to the
  global solar magnetic field. Specific topics discussed include continuum
  observations and empirical models of the thermal structure of sunspots,
  fine structure of umbrae and penumbrae, magnetohydrodynamic waves in
  structural magnetic fields, and the motion of magnetic flux tubes in
  the convection zone and the surface origin of active regions.

Title: The Origin of the Solar Cycle
Authors: Rosner, R.; Weiss, N. O.
Bibcode: 1992ASPC...27..511R
Altcode: 1992socy.work..511R
  No abstract at ADS

Title: What is a stellar dynamo?
Authors: Cattaneo, F.; Hughes, D. W.; Weiss, N. O.
Bibcode: 1991MNRAS.253..479C
Altcode:
  Numerical simulations of turbulent stellar dynamos are now feasible. The
  characteristic time-scale for kinematic behavior is related to the
  turnover time of the turbulent eddies. Results from idealized 2D
  models show that the Lorentz force alters the velocity field, allowing
  transient magnetic activity to persist for intervals much longer than
  the expected turbulent decay time. For 3D flows a characteristic time
  Te is defined for turbulent diffusion to act, based on the rate at which
  magnetic energy is dissipated, and it is asserted that there is a dynamo
  only if the field survives for times much longer than Te. This criterion
  is then applied to cyclic magnetic activity in late-type stars.

Title: Convective structures in the sun
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1991MNRAS.252P...1S
Altcode:
  Observed patterns of motion at the solar surface reflect the structure
  of subphotospheric convection, which controls the distribution of
  angular momentum and magnetic fields. Mesogranules are interpreted
  as secondary features associated with supergranular circulation,
  and that coupling between mesogranules and granulation triggers the
  spasmodic formation of exploding granules. Supergranules are expected
  to generate isolated sinking plumes. It is argued that these plumes
  can penetrate to the base of the convective zone, and that there is
  no organized structure on larger scales.

Title: Symmetry breaking in stellar dynamos
Authors: Jennings, R. L.; Weiss, N. O.
Bibcode: 1991MNRAS.252..249J
Altcode:
  The generation of magnetic fields in stars like the sun can be
  described by an azimuthally averaged dynamo model. Solutions of the
  linear (kinematic) problem have pure dipole or quadrupole symmetry,
  i.e., toroidal fields that are antisymmetric or symmetric about the
  equator. These symmetries can be broken only at bifurcations in the
  nonlinear regime, which lead to the appearance of spatially asymmetric
  mixed-mode solutions. The symmetries of dipole, quadrupole and
  mixed-mode solutions, whether steady or periodic, form the same group
  for any axisymmetric dynamo. To establish the bifurcation structure it
  is necessary to follow unstable as well as stable solutions. This is
  feasible only for simple systems and a minimal nonlinear alpha(omega)
  dynamo is studied in detail in order to illustrate the formation
  of mixed-mode periodic solutions and to distinguish between their
  symmetries. The results are applied to the sun (where there are
  persistent deviations from dipole symmetry) and to other late-type
  stars.

Title: Modeling Mesogranules and Exploders on the Solar Surface
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 1991ApJ...375..775S
Altcode:
  Radial outflows in exploders and mesogranules can be modeled by
  superposing Gaussian source functions. This model is used to explore
  the relationship between mesogranules and exploders. Although it
  is demonstarted that there is a mathematical equivalence between
  mesogranules and exploders distributed normally about the mesogranule
  centers, the results indicate that the observed mesogranular velocity
  pattern is not consistent with a flow pattern generated by exploders
  dropped randomly on the solar surface. Detailed comparisons with
  observations suggest that the averaged mesogranular velocity is produced
  by a combination of a persistent outflow from a source together with
  exploders distributed randomly about its center. Similar analysis
  also shows supergranules are not the result of random occurrences
  of mesogranules.

Title: Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 1991GApFD..62..229W
Altcode:
  Cowling investigated the effect of an imposed magnetic field on
  convection in order to explain the origin of sunspots. After summarizing
  the classical linear theory of Boussinesq magnetoconvection, this review
  proceeds to more recent nonlinear results. Weakly nonlinear theory is
  used to establish the relevant bifurcation structure, which involves
  steady, oscillatory and chaotic solutions. Behaviour found in numerical
  experiments can then be related to these analytical results. Thereafter,
  attention is focused on the astrophysically relevant problem of fully
  compressible magnetoconvection. Steady two-dimensional nonlinear
  solutions show two important effects: stratification introduces an
  asymmetry between rising and falling fluid, while compressibility
  leads to evacuated magnetic flux sheets. Time-dependent behaviour
  includes transitions between standing waves and travelling waves,
  as well as changes in horizontal scale, leading to the development of
  more complicated spatial structures. Work on three-dimensional models,
  which is now in progress, will lead to a better understanding of the
  structure of a sunspot.

Title: Simulating exploding granules and mesogranular flows
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 1991AdSpR..11e.259S
Altcode: 1991AdSpR..11..259S
  Cellular convective motion at the solar surface can be simulated by a
  suitable distribution of axisymmetric sources /1/. With this model we
  represent randomly distributed exploding granules or mesogranules. The
  effect of a given velocity field on the magnetic field is modelled
  by inserting test particles (``corks'') and following their resultant
  motions. An important question raised by the observations is whether
  mesogranular flows are generated entirely by exploding granules
  which recur in approximately the same location or whether there is a
  persistent underlying circulation. <P />Our model calculations suggest
  that a combination of systematic cellular motion on a mesogranular scale
  and recurrent exploding granules located near the mesogranular centers
  is compatible with observed magnetic structures. We also generate
  randomly-distributed exploders not tethered to mesogranular sites, and
  the resulting cork patterns do not resemble those observed on the solar
  surface. Finally we introduce a large-scale persistent supergranular
  flow which transports the mesogranules and exploders towards the
  supergranular network and obtain patterns not unlike those seen on
  the Sun. <P />Operated by the National Optical Astronomy Observatories
  for the Association of Universities for Research in Astronomy, Inc.,
  under contract with the National Science Foundation. Partial Support
  for the National Solar Observatory is provided by the USAF under a
  Memorandum of Understanding with the NSF.

Title: Momentum boundary conditions and Euclidean field theory
Authors: Unruh, W. G.; Weiss, N.
Bibcode: 1990CQGra...7.2331U
Altcode:
  No abstract at ADS

Title: Kinematic Modeling of the Relations Among Exploders,
    Mesogranules, and Supergranules
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
Bibcode: 1990BAAS...22R1225S
Altcode:
  No abstract at ADS

Title: Oscillatory convection in sunspot umbrae
Authors: Weiss, N. O.; Brownjohn, D. P.; Hurlburt, N. E.; Proctor,
   M. R. E.
Bibcode: 1990MNRAS.245..434W
Altcode:
  Subphotospheric convection is partially inhibited by the strong
  vertical magnetic field at the centre of a sunspot. We investigate
  the effects of stratification on non-linear magnetoconvection in a
  fully compressible perfect gas by means of two-dimensional numerical
  experiments. Behaviour depends critically on the ratio ξ of the
  magnetic to the thermal diffusivity, which increases with depth. If
  ξ &gt; 1 throughout the layer we find steady overturning convection
  with an asymmetry between rising and falling plumes. For ξ &gt; 1
  we obtain oscillatory convection with reversals of the flow. When ξ
  &gt; 1 at the top of the layer but ξ &gt; 1 at its base, convection
  sets in as steady motion but there is a transition (involving several
  bifurcations) to mixed-mode periodic solutions as the Rayleigh number
  is increased. The flow at the bottom of the layer does not reverse
  but adjacent rising plumes alternate between active and quiescent
  states. In the umbral photosphere t, &gt; 1 but ξ &gt; 1 at depths
  below 1500 km owing to the increase in opacity. Our results imply that
  time-dependent convection immediately below the photosphere is coupled
  to motion at levels where ξ &gt; 1. They also explain the existence
  of umbral dots with a lifetime corresponding to the Alfven time for
  the converting layer.

Title: Solar and stellar convection zones.
Authors: Weiss, N. O.
Bibcode: 1990CoPhR..12..233W
Altcode:
  There are several important astrophysical questions that might be
  answered by numerical modelling. These involve the kinematic effects
  of motion on magnetic fields, the dynamics of magnetoconvection, the
  structure and scale of convection and the global dynamo problem. This
  review focuses on detailed modelling of nonlinear compressible
  convection in a strong vertical magnetic field. Techniques range
  from heuristic models, which may be relatively primitive, through
  idealized experiments to large scale simulations and each approach
  has its proponents. There have been systematic investigations of
  fully compressible two- and three-dimensional convection as well as
  ambitious simulations. Detailed studies of two-dimensional behaviour
  reveal complicated bifurcation structures, involving changes of scale
  and transitions from steady to oscillatory solutions and from standing
  waves to travelling waves. Models of large-scale behaviour throughout
  the convection zone of a star like the sun show that dynamo action
  can occur but are still far from being able to reproduce the observed
  patterns of differential rotation or magnetic activity.

Title: Fine structure on the Sun
Authors: Weiss, Nigel
Bibcode: 1990Natur.344..815W
Altcode:
  No abstract at ADS

Title: Periodicity and Aperiodicity in Solar Magnetic Activity
Authors: Weiss, N. O.
Bibcode: 1990RSPTA.330..617W
Altcode:
  Solar activity varies irregularly with an 11-year period whereas the
  magnetic cycle has a period of 22 years. Similar cycles of activity
  are seen in other slowly rotating late-type stars. The only plausible
  theory for their origin ascribes them to a hydromagnetic dynamo
  operating at, or just below, the base of the convective zone. Linear
  (kinematic) dynamo models yield strictly periodic solutions with
  dynamo waves propagating towards or away from the equator. Nonlinear
  (magneto-hydrodynamic) dynamo models allow transitions from periodic to
  quasi-periodic to chaotic behaviour, as well as loss of spatial symmetry
  followed by the development of complex spatial structure. Results from
  simple models can be compared with the observed sunspot record over
  the past 380 years and with proxy records extending over 9000 years,
  which show aperiodic modulation of the 11-year cycle.

Title: Symmetry Breaking in the Solar Dynamo: Nonlinear Solutions
Authors: Jennings, R. L.; Weiss, N. O.
Bibcode: 1990IAUS..138..355J
Altcode:
  No abstract at ADS

Title: Magnetohydrodynamics of Sunspots
Authors: Weiss, N. O.
Bibcode: 1990IAUS..142..139W
Altcode:
  Recent numerical investigations of fully compressible nonlinear
  magnetoconvection have clarified the nature of convection in sunspot
  umbrae. In a shallow layer with a strong vertical magnetic field
  oscillations give way to traveling waves as the Rayleigh number is
  increased but in a deep stratified layer oscillatory behavior only
  appears after secondary bifurcations. This behavior leads to a model
  that explains the formation of umbral dots. Penumbral structure is
  more difficult to explain owing to the apparent presence of adjacent
  horizontal and inclined fields in dark and bright filaments. The inner
  penumbra lies above a transition zone where volume currents are needed
  to maintain an overall static equilibrium; instabilities in this region
  may be responsible for filamentary structure in the penumbra as well
  as for fine structure at the umbral-penumbral boundary.

Title: Transitions to asymmetry in magnetoconvection
Authors: Nagata, M.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1990GApFD..51..211N
Altcode:
  In two-dimensional Boussinesq magnetoconvection with symmetrical
  boundary conditions upward and downward motion are equivalent. Hence
  there exist symmetric solutions with equivalent flux sheets on either
  side of each convection roll. Numerical experiments show that this
  symmetry can be broken for both steady and oscillatory solutions. The
  underlying bifurcation structure is established by studying a truncated
  seventeenth-order model system. Steady solutions of this relatively
  low-order system can be obtained explicitly and their stability can be
  investigated. Primary bifurcations from the trivial static solution lead
  to pure single-roll and two-roll solutions, both steady and oscillatory;
  secondary bifurcations give mixed-mode steady and oscillatory branches
  while tertiary bifurcations allow behaviour that is more complicated but
  less robust. Properly interpreted, this detailed study of a particular
  system provides a better understanding of the behaviour of nonlinear
  solutions of the full partial differential equations.

Title: Periodicity and aperiodicity in solar magnetic activity.
Authors: Weiss, N. O.
Bibcode: 1990ecvs.conf..617W
Altcode:
  Solar activity varies irregularly with an 11-year period whereas the
  magnetic cycle has a period of 22 years. Similar cycles of activity
  are seen in other slowly rotating late-type stars. The only plausible
  theory for their origin ascribes them to a hydromagnetic dynamo
  operating at, or just below, the base of the convective zone. Linear
  (kinematic) dynamo models yield strictly periodic solutions with
  dynamo waves propagating towards or away from the equator. Nonlinear
  (magnetohydrodynamic) dynamo models allow transitions from periodic to
  quasi-periodic to chaotic behaviour, as well as loss of spatial symmetry
  followed by the development of complex spatial structure. Results from
  simple models can be compared with the observed sunspot record over
  the past 380 years and with proxy records extending over 9000 years,
  which show aperiodic modulation of the 11-year cycle.

Title: Nonlinear compressible magnetoconvection. I - Travelling
    waves and oscillations
Authors: Hurlburt, N. E.; Proctor, M. R. E.; Weiss, N. O.; Brownjohn,
   D. P.
Bibcode: 1989JFM...207..587H
Altcode:
  Two-dimensional compressible convection in a polytropic layer with an
  imposed vertical magnetic field is studied in a series of numerical
  experiments which consider a shallow layer, spanning only a fraction
  of a scale height in density, and increase the ratio (1/beta) of the
  magnetic to the thermal pressure in a regime where convection sets in
  at an oscillatory bifurcation. Initially, there are stable periodic
  oscillations (standing wave solutions). For moderate values of beta
  the only deviations from Boussinesq behavior are where the field is
  locally intense but as beta is decreased magnetic pressure fluctuations
  become increasingly important. When beta is of order unity at the top
  of the layer standing waves become unstable at higher Rayleigh numbers
  and traveling waves are preferred. This is an essentially compressible
  effect in which magnetic pressure plays a crucial role. The associated
  bifurcation structure is investigated in some detail.

Title: Simulation of Large-Scale Flows at the Solar Surface
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1989ApJ...345.1060S
Altcode:
  A simple analytic axisymmetric function is used to represent the radial
  outflow associated with an isolated convection plume at the solar
  surface. The vertical velocity can be deduced from the continuity
  equation. A regular cellular pattern of convection can be created
  by superposing a number of such sources. The function is applied
  to the large-scale horizontal motions observed by the Solar Optical
  Universal Polarimeter (SOUP) instrument on Spacelab 2. The flow pattern
  visible in three different regions covered by the SOUP observations
  is simulated. In each case a superposition of the plume functions
  mimics the observed mesogranular and supergranular motions well. The
  model flows are used to compute the motion of passive test particles
  (corks) which accumulate in a network that outlines mesogranular
  cells. Detailed comparisons suggest that magnetic flux tubes are
  affected more by outflow from sources at the centers of mesogranules
  than by flow into sinks within the network.

Title: Simulating plumes and sinks observed at the solar surface
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1989hsrs.conf..529S
Altcode:
  No abstract at ADS

Title: Modeling the Flow in Solar Vortices
Authors: Simon, G. W.; Weiss, N. O.; Scharmer, G. B.
Bibcode: 1989BAAS...21Q.829S
Altcode:
  No abstract at ADS

Title: Time Dependent Compressible Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 1989ASIC..263..471W
Altcode: 1989ssg..conf..471W
  No abstract at ADS

Title: Compressible Magnetoconvection
Authors: Weiss, N. O.
Bibcode: 1989gmca.conf....1W
Altcode:
  No abstract at ADS

Title: A Simple Model of Mesogranular and Supergranular Flows
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1989ASIC..263..595S
Altcode: 1989ssg..conf..595S
  No abstract at ADS

Title: Dynamo Processes in Stars
Authors: Weiss, N. O.
Bibcode: 1989ASSL..156...11W
Altcode: 1989admf.proc...11W
  Present understanding of stellar dynamo processes is reviewed. The
  observational constraints are described, and the basic physical
  processes of helicity and differential rotation that lead to
  dynamo action are outlined, stressing the importance of recent
  helioseismological results. Mean field dynamo theory and nonlinear
  dynamo waves are discussed.

Title: Simulation of Large-Scale Flows at the Solar Surface
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1988BAAS...20.1008S
Altcode:
  No abstract at ADS

Title: Is the solar cycle an example of deterministic chaos?
Authors: Weiss, N. O.
Bibcode: 1988ssgv.conf...69W
Altcode:
  No abstract at ADS

Title: The relation between convection flows and magnetic structure
    at the solar surface
Authors: Simon, G. W.; November, L. J.; Acton, L. W.; Title, A. M.;
   Tarbell, T. D.; Topka, K. P.; Shine, R. A.; Ferguson, S. H.; Weiss,
   N. O.; Zirin, H.
Bibcode: 1988AdSpR...8k.133S
Altcode: 1988AdSpR...8..133S
  We describe recent results from the comparison of data from the Solar
  Optical Universal Polarimeter instrument on Spacelab 2 and magnetograms
  from Big Bear Solar Observatory. We show that the Sun's surface velocity
  field governs the structure of the observed magnetic field over the
  entire solar surface outside sunspots and pores. We attempt to describe
  the observed flows by a simple axisymmetric plume model. Finally,
  we suggest that these observations may have important implications
  for the prediction of solar flares, mass ejections, and coronal heating.

Title: Dynamics of Convection
Authors: Weiss, N. O.
Bibcode: 1987RSPSA.413...71W
Altcode:
  Thermal convection in a fluid layer is an example of a dynamical system
  governed by partial differential equations. As the relevant control
  parameter (the Rayleigh number) is increased, successive bifurcations
  may lead to chaos and the nature of the transition depends on the
  spatial structure of the flow. Numerical experiments with idealized
  symmetry and boundary conditions make it possible to explore nonlinear
  behaviour in some detail and to relate bifurcation structures to
  those found in appropriate low-order systems. Two examples are used
  to illustrate transitions to chaos. In two-dimensional thermosolutal
  convection, where the spatial structure is essentially trivial,
  chaos is caused by a heteroclinic bifurcation involving a symmetric
  pair of saddle foci. When convection is driven by internal heating
  several competing spatial structures are involved and the transition
  to chaos is more complicated in both two-and three-dimensional
  configurations. Although the first few bifurcations can be isolated a
  statistical treatment is needed for behaviour at high Rayleigh numbers.

Title: Magnetic fields and non-uniform rotation in stellar radiatives
    zones.
Authors: Mestel, L.; Weiss, N. O.
Bibcode: 1987MNRAS.226..123M
Altcode:
  This paper examines the effects of dynamical and resistive instabilities
  on magnetic redistribution of angular momentum within a star. It is
  tentatively concluded that if significant differential rotation survives
  in a stably stratified radiative zone over a stellar evolution time,
  then the poloidal field, B<SUB>p</SUB>, cannot exceed an upper limit of
  order 3×10<SUP>-2</SUP>G and is probably less than 10<SUP>-3</SUP>G. In
  the radiative core of the Sun B<SUB>p</SUB> is estimated to be at
  least of order 5×10<SUP>-2</SUP>G and probably 100 G or more. Values
  greater than 0.1 G cannot easily be reconciled with the rotational
  shear inferred from frequency splitting of solar oscillations.

Title: Rotation and magnetic fields in the Sun.
Authors: Weiss, N. O.
Bibcode: 1987ppcs.work...46W
Altcode:
  Stellar magnetic fields exert torques which alter the distribution of
  angular momentum in a star. In the radiative interior of the sun, these
  torques tend to enforce uniform rotation and the existence of a rapidly
  rotating core would imply a poloidal field of less than 0.01 G. In
  the convective envelope, magnetic fields generated by dynamo action
  produce torques which lead to torsional oscillations. A simple nonlinear
  model allows both multiply periodic and chaotic behavior. This system
  demonstrates that both aperiodic magnetic cycles and the irregular
  modulation responsible for grand minima can be regarded as examples of
  deterministic chaos. This picture is consistent with the C-14 record
  but implies that the multiply periodic lamination of some Precambrian
  varves is not associated with the solar cycle.

Title: What can the sun tell us about stellar activity?
Authors: Weiss, N. O.
Bibcode: 1987LNP...292....1W
Altcode:
  The solar-stellar connection relates high-resolution synoptic solar
  observations to observations of magnetic activity in stars with
  different rotation rates and internal structures. Our knowledge of
  magnetic fields in stellar convection zones is based on detailed
  observations of field structures in the Sun but recent measurements
  of magnetic activity in other late-type stars have extended
  our understanding of the solar dynamo. These observations have
  stimulated detailed modelling of processes associated with magnetic
  activity. Modulation of activity cycles in slowly rotating stars can
  be inferred from terrestrial data extending over the last 104 years,
  while the evolution of the Sun's magnetic field can be inferred from
  the behaviour of younger stars.

Title: What Can the Sun Tell Us About Stellar Activity?
Authors: Weiss, N. O.
Bibcode: 1987LNP...292....3W
Altcode: 1987ssp..conf....3W
  The solar-stellar connection relates high-resolution synoptic
  solar observations to observations of magnetic activity in stars
  with different rotation rates and internal structures. Modulation
  of activity cycles in slowly rotating stars can be inferred from
  terrestrial data extending over the last 10<SUP>4</SUP>years, while
  the evolution of the Sun's magnetic field can be inferred from the
  behaviour of younger stars.

Title: Dynamical chaos. Proceedings of a Royal Society discussion
    meeting held in London, UK, 4 - 5 February 1987.
Authors: Berry, M. V.; Percival, I. C.; Weiss, N. O.; Zeeman, E. C.
Bibcode: 1987dcpr.book.....B
Altcode:
  The individual contributions within the subject scope of Astronomy and
  Astrophysics Abstracts are included in their corresponding categories -
  see abstracts 015.003, 021.002, 021.003, 022.002 - 022.005, 062.006 -
  062.009, 091.002.

Title: Interaction between Magnetic Fields and Convection
Authors: Hurlburt, N. E.; Weiss, N. O.
Bibcode: 1987rfsm.conf...35H
Altcode:
  The authors discuss nonlinear convection in the presence of an imposed
  vertical magnetic field and its influence on the fine structure of the
  resulting field. They contrast recent results of numerical experiments
  on steady and oscillatory magnetoconvection with those obtained in the
  Boussinesq approximation. An attempt is also made to relate idealized
  model calculations to the structure of observed magnetic fields in
  the solar photosphere.

Title: Simulation of Surface Flows in Supergranulation
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1986BAAS...18R.990S
Altcode:
  No abstract at ADS

Title: Energy transport in sunspot penumbrae.
Authors: Schmidt, H. U.; Spruit, H. C.; Weiss, N. O.
Bibcode: 1986A&A...158..351S
Altcode:
  It is proposed that the magnetic field in the outer penumbra of a
  sunspot is almost horizontal and that the penumbra itself is very
  shallow, with a sharp lower boundary. A simple model of energy transport
  in the outer penumbra predicts that there is a Wilson depression
  of about 100 km, below which the penumbra extends for only 80 km. A
  two-component model with bright and dark filaments suggests that the
  associated differences in observed field strength and corrugations
  of the visible surface of the penumbra will be small. The authors
  argue that flows along the field are needed to explain the existence
  of bright and dark filaments while the Evershed flow is driven by
  pressure differences along flux tubes.

Title: Magnetic torques and differential rotation.
Authors: Weiss, N. O.
Bibcode: 1986ASIC..169..253W
Altcode: 1986ssds.proc..253W
  The rotation profile deduced from the measured splitting of solar
  oscillations raises several problems. The slight decrease in angular
  velocity within the convective zone can be explained and the transition
  from differential to uniform rotation on spherical surfaces must cause
  a further reduction in the radiative zone. The bump, associated with
  harmonics of degree 11, seems implausible and it is hard to reconcile
  a rapidly rotating core with the presence of a significant magnetic
  field. A possible explanation is that this core has been magnetically
  decoupled from outer regions since the Sun evolved on to the Hayashi
  track.

Title: Stellar dynamo characteristics
Authors: Weiss, N. O.
Bibcode: 1986HiA.....7..385W
Altcode:
  Recent discoveries have shown that magnetic activity is typical of
  cool stars with deep convective zones and magnetic cycles are found in
  slowly rotating stars like the sun. The current state of hydromagnetic
  dynamo theory is reviewed, and simplified models are used in an attempt
  to isolate the dominant nonlinear processes in stellar dynamos.

Title: Differential rotation and magnetic torques in the interior
    of the Sun
Authors: Rosner, R.; Weiss, N. O.
Bibcode: 1985Natur.317..790R
Altcode:
  The frequencies of solar oscillations can be measured with extreme
  precision and 5-min oscillations reveal the internal structure of
  the Sun<SUP>1-5</SUP>. In particular, measurements of rotational
  splitting<SUP>4</SUP> have provided the first reliable indications of
  the variation of angular velocity with radius<SUP>6</SUP>, while recent
  observations<SUP>5</SUP> have yielded information on the variation
  with depth of latitudinal differential rotation. These results confirm
  theoretical predictions that the angular velocity decreases inwards in
  the convective zone<SUP>7,8</SUP> but raise problems for dynamo models
  of the solar cycle. The suggestion that the core rotates with roughly
  twice the surface angular velocity has important implications both
  for the rotational history of the Sun and for other late-type stars,
  whose magnetic activity is closely correlated with rotation. Such a
  rapidly rotating core is hard to reconcile with the presence of any
  significant magnetic field pervading the entire radiative interior. We
  can only explain it by suggesting that the core contains a fossil
  field, unaffected by turbulence in the pre-main sequence Hayashi phase,
  that is decoupled from the rest of the star.

Title: Oscillatory Convection in Flux Tubes Pores and Sunspots
Authors: Hurlburt, N.; Weiss, N. O.
Bibcode: 1985tphr.conf..198H
Altcode:
  No abstract at ADS

Title: Buoyant magnetic flux tubes. II - Three-dimensional behaviour
    in granules and supergranules
Authors: Schmidt, H. U.; Simon, G. W.; Weiss, N. O.
Bibcode: 1985A&A...148..191S
Altcode:
  A simple model is used to study the interaction of isolated magnetic
  flux tubes with convection in the sun. Convective motion in granules and
  supergranules is represented by prescribed flows in three-dimensional
  cells with square cross-sections and thin flux tubes move under the
  action of magnetic buoyancy, Lorentz curvature forces and aerodynamic
  drag. Inflow at the base of a cell competes with outflow at its upper
  surface; small flux tubes tend to be swept to the cell boundaries while
  larger, more buoyant tubes are dragged to the axis of the cell. These
  results are compared with recent observations of small-scale granular
  and intergranular magnetic fields.

Title: Chaotic behavior in stellar dynamos
Authors: Weiss, N. O.
Bibcode: 1985JSP....39..477W
Altcode:
  Slowly rotating main-sequence stars with deep convective zones have
  activity cycles like the sun's. The solar cycle is aperiodic and
  modulated to give intervals of reduced activity. A simple sixth-order
  system, obtained by truncating the dynamo equations, has solutions
  that mimic this behavior. The transition to chaos is analyzed and the
  astrophysical significance of these results is discussed.

Title: Book-Review - the Solar Granulation
Authors: Bray, R. J.; Loughhead, R. E.; Durrant, C. J.; Weiss, N. O.
Bibcode: 1985SoPh...96..423B
Altcode:
  No abstract at ADS

Title: Book review
Authors: Weiss, N. O.
Bibcode: 1985SoPh...96..423W
Altcode:
  No abstract at ADS

Title: 3-D Behavior of Buoyant Magnetic Flux Tubes in Granules and
    Supergranules
Authors: Simon, G. W.; Schmidt, H. U.; Weiss, N. O.
Bibcode: 1985BAAS...17Q.642S
Altcode:
  No abstract at ADS

Title: Oscillatory convection in flux tubes, pores and sunspots.
Authors: Hurlburt, N. E.; Weiss, N. O.
Bibcode: 1985MPARp.212..198H
Altcode:
  High-resolution images of the solar surface provide a means for probing
  sub-photospheric structures. The authors combine simple conceptual
  arguments with numerical models to consider the different flow regimes
  possible within flux tubes, pores and sunspots which should be found
  in detailed observations. In the presence of a strong magnetic field
  convection near the photosphere is likely to be oscillatory. The
  authors have carried out a series of numerical experiments involving
  simple atmospheres (polytropic in the absence of convection).

Title: Nonlinear dynamos: A complex generalization of the Lorenz
    equations
Authors: Jones, C. A.; Weiss, N. O.; Cattaneo, F.
Bibcode: 1985PhyD...14..161J
Altcode:
  Plane nonlinear dynamo waves can be described by a sixth order system
  of nonlinear ordinary differential equations which is a complex
  generalization of the Lorenz system. In the regime of interest
  for modelling magnetic activity in stars there is a sequence of
  bifurcations, ending in chaos, as a stability parameter D (the
  dynamo number) is increased. We show that solutions undergo three
  successive Hopf bifurcations, followed by a transition to chaos. The
  system possesses a symmetry and can therefore be reduced to a fifth
  order system, with trajectories that lie on a 2-torus after the
  third bifurcation. As D is then increased, frequency locking occurs,
  followed by a sequence of period-doubling bifurcations that leads to
  chaos. This behaviour is probably caused by the Shil'nikov mechanism,
  with a (conjectured) homoclinic orbit when D is infinite.

Title: Energy transport in sunspot penumbrae.
Authors: Schmidt, H. U.; Spruit, H. C.; Weiss, N. O.
Bibcode: 1985MPARp.182.....S
Altcode:
  No abstract at ADS

Title: Theoretical Interpretation of Small-Scale Solar Features
Authors: Weiss, N. O.
Bibcode: 1985LNP...233..217W
Altcode: 1985hrsp.proc..217W
  The structure of photospheric magnetic fields is dominated by the
  interaction between granular convection and isolated flux tubes. The
  current understanding of compressible convection, and of both kinematic
  and dynamical aspects of magnetoconvection is summarized. These theories
  are related to the formation and location of intense magnetic fields
  within the photospheric network. The overall structure of sunspots is
  reconsidered and related to umbral and penumbral features.

Title: Magnetoconvection.
Authors: Weiss, N. O.
Bibcode: 1985ssmf.conf..156W
Altcode:
  The author focuses on three topics. These are, first, the formation of
  small flux tubes; second, the nature of convection in a strong magnetic
  field; and, third, the structure of the large-scale magnetic field in
  the sun.

Title: The relation between stellar rotation rate and activity
    cycle periods.
Authors: Noyes, R. W.; Weiss, N. O.; Vaughan, A. H.
Bibcode: 1984ApJ...287..769N
Altcode:
  The empirical relation between rotation period, spectral type, and
  cycle activity period in 13 slowly rotating main-sequence stars is
  investigated, on the basis of available spectrometric data. It is
  shown that for slowly rotating stars with similar spectral types, the
  cycle period P(cyc), and rotation period P(rot) were related such that
  P(cyc) varies as P(rot) to the nth, where n equals 1.25. In a group of
  stars with individual spectral types from G2 to K7, the cycle periods
  were consistent with the relation P(cyc) is approximately equal to (P
  rot/tau<SUB>c)</SUB> exp n, where tau<SUB>c</SUB> is the convective
  turnover time near the bottom of the convection zone. On the basis
  of the above relations, it is suggested that an increase of P(cyc)
  with increasing P(rot) does not agree with conventional estimates from
  nonlinear dynamo models, and is limited by two factors: the quenching
  of the alpha effect; and differential rotation.

Title: Amplification and maintenance of thin magnetic flux tubes by
    compressible convection.
Authors: Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1984ESASP.220...77P
Altcode: 1984ESPM....4...77P
  The authors present a model that includes both the effects of diffusion
  and proper treatment of the Lorentz forces, for a thin tube whose depth
  is of the order of a scale height. The model includes both magnetic
  pressure (leading to evacuation of the tube) and curvature forces. It
  is found that while small tubes are limited principally by pressure
  effects, tubes with fluxes ≡10<SUP>18</SUP>mx exert an important
  retarding force on the convection that causes them.

Title: Convection in sunspots and the origin of umbral dots
Authors: Knobloch, E.; Weiss, N. O.
Bibcode: 1984MNRAS.207..203K
Altcode:
  Recent studies of non-linear magnetoconvection are used to show that
  the observed properties of umbral dots can be explained if they are
  produced by oscillatory convection in the umbrae of sunspots. The
  overall magnetic field is assumed to be coherent within the flux tube
  underneath the sunspot. Individual convection cells are about 1500 km
  deep and 300 km in diameter. The oscillations are highly non-linear,
  with periods of around 6 hr, but the relatively vigorous upward motion
  that is responsible for umbral dots lasts for only a fraction of this
  lifetime. This model is compared with various alternative hypotheses.

Title: Periodic and aperiodic dynamo waves
Authors: Weiss, N. O.; Cattaneo, F.; Jones, C. A.
Bibcode: 1984GApFD..30..305W
Altcode:
  In order to show that aperiodic magnetic cycles, with Maunder
  minima, can occur naturally in nonlinear hydromagnetic dynamos, we
  have investigated a simple nonlinear model of an oscillatory stellar
  dynamo. The parametrized mean field equations in plane geometry have a
  Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo
  waves. Including the nonlinear interaction between the magnetic field
  and the velocity shear results in a system of seven coupled nonlinear
  differential equations. For D&gt;1 there is an exact nonlinear
  solution, corresponding to periodic dynamo waves. In the regime
  described by a fifth order system of equations this solution remains
  stable for all D and the velocity shear is progressively reduced by
  the Lorentz force. In a regime described by a sixth order system, the
  solution becomes unstable and successive transitions lead to chaotic
  behaviour. Oscillations are aperiodic and modulated to give episodes
  of reduced activity.

Title: Problems of Flux Tube Formation
Authors: Weiss, N. O.
Bibcode: 1984ssdp.conf..287W
Altcode:
  Recent theoretical studies of magnetoconvection predict that strong
  fields will be formed between granules but also suggest that much of
  the magnetic flux may remain near the center of a granule.

Title: Solar and stellar magnetic fields
Authors: Priest, E. R.; Weiss, N. O.
Bibcode: 1983Obs...103..239P
Altcode:
  No abstract at ADS

Title: Simple models for magnetic flux tubes.
Authors: Simon, G. W.; Weiss, N. O.; Nye, A. H.
Bibcode: 1983SoPh...87...65S
Altcode:
  Known potential field solutions can be used to model the structure of
  magnetic fields in the solar photosphere. Several two-dimensional and
  axisymmetric solutions are compared. In the most satisfactory model
  the vertical component of the field is prescribed on a horizontal
  plane so as to be uniform within a finite disc and zero outside it. The
  resulting flux distribution provides a good description of small scale
  intergranular magnetic fields and of the observed field structure in
  a pore, but is inadequate for sunspots.

Title: A review of: "Finite-difference techniques for vectorized
    fluid dynamics calculations"
Authors: Weiss, N. O.
Bibcode: 1983GApFD..23..344W
Altcode:
  Edited by D. L. Book. Springer-Verlag, New York, 1981. 226 pp., DM 72,
  - , $33.60. (ISBN 0 387 104828)

Title: Solar magnetism
Authors: Weiss, N. O.
Bibcode: 1983spm..conf..115W
Altcode:
  Magnetic fields in the Sun and other late-type stars follow cycles of
  activity, which are more vigorous in rapidly rotating stars. Mean-field
  dynamo theory provides a good qualitative description of these magnetic
  cycles, though it cannot be justified in detail. Future progress will
  require more elaborate models, related to observations and relying
  heavily on computation.

Title: Simple models for magnetic flux tubes.
Authors: Simon, G. W.; Weiss, N. O.; Nye, A. H.
Bibcode: 1983BAAS...15R.874S
Altcode:
  No abstract at ADS

Title: Future research directions - Theoretical approach and
    perspective
Authors: Weiss, N. O.
Bibcode: 1983ASSL..102..639W
Altcode: 1983IAUCo..71..639W; 1983ards.proc..639W
  Theoretical aspects of magnetic activity in red dwarfs are
  surveyed. Some general remarks about the role of theory in astrophysics
  are made, and a phenomenological description of red dwarf magnetic
  fields is briefly presented. Numerical simulation of nonlinear processes
  in magnetic fields is illustrated with examples of stellar dynamos,
  turbulent magnetic fields, and the interaction of magnetic fields
  with granular convection. Examples of simplified problems that can
  be solved by some combination of analytical or numerical techniques
  as an alternative to large scale simulations are given, including
  problems involving alpha-omega dynamo models, formation of flux ropes
  by magnetic buoyancy, and isolated flux tubes.

Title: Periodic and aperiodic behaviour in stellar dynamos
Authors: Cattaneo, F.; Weiss, N. O.; Jones, C. A.
Bibcode: 1983IAUS..102..307C
Altcode:
  A simple parameterized mean field dynamo model has been constructed
  that includes the dynamical interaction between the magnetic field and
  differential rotation. This system of seven coupled nonlinear ordinary
  differential equations has finite amplitude oscillatory solutions
  (corresponding to Parker's dynamo waves) when the dynamo number (D)
  is greater than one. Two regimes were studied. In the first, the
  velocity shear is reduced by the Lorentz force and there are stable
  periodic solutions for all dynamo numbers greater than one. In the
  second there is a transition from strictly periodic oscillations to
  aperiodic (chaotic) behavior as D is increased. This simple example
  shows that nonlinear hydromagnetic dynamos can produce aperiodic cycles,
  with Maunder minima, as observed in the sun and other late-type stars.

Title: Magnetic buoyancy and the Boussinesq approximation
Authors: Spiegel, E. A.; Weiss, N. O.
Bibcode: 1982GApFD..22..219S
Altcode:
  The full Boussinesq equations for hydromagnetic convection are derived
  and shown to include the effects of magnetic buoyancy. Instabilities
  caused by magnetic buoyancy are analyzed and their roles in double
  convection are brought out.

Title: REVIEW ARTICLE: Magnetoconvection
Authors: Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1982RPPh...45.1317P
Altcode:
  The interaction between convection and an externally imposed magnetic
  field in a Boussinesq fluid is discussed. The equations that govern
  Boussinesq magnetoconvection are derived and boundary conditions
  and simplified geometries are discussed. The kinematic effects
  of prescribed velocity fields on magnetic fields, including flux
  expulsion and the formation of isolated sheets or tubes of flux, are
  treated. Dynamical effects are introduced by considering the simpler
  Oberbeck problem and demonstrating the exclusion of motion from the
  flux sheets. Linear stability theory for the Rayleigh-Benard problem is
  summarized. Two-dimensional magnetoconvection is discussed in detail;
  results obtained by perturbation methods are described and extended
  into the nonlinear regime by adopting a truncated model system, and
  numerical results for the full problem are presented. Axisymmetric
  magnetoconvection is described, and the transition from the
  kinematic regime to one in which the field is dynamically active is
  discussed. Extensions of the theory to more exotic effects are briefly
  reviewed, and astrophysical implications are briefly commented on.

Title: Magnetic fields in late-type stars
Authors: Knobloch, E.; Rosner, R.; Weiss, N. O.
Bibcode: 1981MNRAS.197P..45K
Altcode:
  Observations show that magnetic activity in late-type stars is
  correlated with rotation rates and that there is a discontinuous change
  in behavior at a critical rotation period. This can be explained as
  a consequence of a transition from convection in rolls parallel to
  the rotation axis to normal convection cells as the angular velocity
  is decreased.

Title: The interplay between magnetic fields and convection
Authors: Weiss, N. O.
Bibcode: 1981JGR....8611689W
Altcode:
  The development of hydrodynamic dynamo theory is considered, taking into
  account investigations related to the solar cycle. Before constructing
  any detailed models of the solar cycle it is necessary to understand
  both the kinematic effect of convection on the magnetic field and the
  dynamical effect of the distorted field on the motion. The effect of a
  convective eddy on the magnetic field can be explored by studying an
  isolated sphere or cylinder rotating as a solid body in an otherwise
  uniform field. It is shown that reconnection of the lines of force leads
  to flux expulsion. A summary is provided of the relevant aspects of
  magnetoconvection, and a description is presented of some new results,
  obtained from numerical experiments at fairly high Rayleigh numbers. The
  computations illustrate the complexity of the nonlinear interaction
  between magnetic fields and convection.

Title: Convection and magnetic fields in late-type stars.
Authors: Weiss, N. O.
Bibcode: 1981Obs...101...37W
Altcode:
  No abstract at ADS

Title: Convection and magnetic fields in stars
Authors: Galloway, D. J.; Weiss, N. O.
Bibcode: 1981ApJ...243..945G
Altcode:
  Recent observations have demonstrated the unity of the study of stellar
  and solar magnetic fields. Results from numerical experiments on
  magnetoconvection are presented and used to discuss the concentration
  of magnetic flux into isolated ropes in the turbulent convective
  zones of the sun or other late-type stars. Arguments are given for
  siting the solar dynamo at the base of the convective zone. Magnetic
  buoyancy leads to the emergence of magnetic flux in active regions, but
  weaker flux ropes are shredded and dispersed throughout the convective
  zone. The observed maximum field strengths in late-type stars should
  be comparable with the field that balances the photospheric pressure.

Title: Stellar magnetic structure and activity (theory).
Authors: Weiss, N. O.
Bibcode: 1981ASIC...68..449W
Altcode: 1981spss.conf..449W
  Both the overall behavior of the solar cycle and the underlying
  fine structure of magnetic fields in the sun have been studied
  mathematically in some detail. These theories are summarized and
  different phenomenological models of the solar cycle are reviewed. In
  order to provide a description of the magnetic fields in late-type
  stars it is necessary to extrapolate boldly from what is known about the
  sun. In this way field strengths and configurations can be estimated.

Title: Solar magnetic fields - The generation of emerging flux
Authors: Golub, L.; Rosner, R.; Vaiana, G. S.; Weiss, N. O.
Bibcode: 1981ApJ...243..309G
Altcode:
  X-ray observations have provided information about magnetic fields on
  the sun, and the implications of these observations are discussed. The
  pattern of small-scale flux emergence is quite different from that of
  active regions. It is inferred that the small-scale fields originate
  fairly high in the convective zone, while the fields in active regions
  have a deeper origin. The small-scale turbulent fields are only loosely
  related to the fields that define the normal solar cycle. The way in
  which dynamo models must be modified in the light of these results
  is indicated.

Title: Large aspect ratio cells in two-dimensional thermal convection
Authors: Hewitt, J. M.; McKenzie, D. P.; Weiss, N. O.
Bibcode: 1980E&PSL..51..370H
Altcode:
  Numerical experiments have been carried out on two-dimensional thermal
  convection, in a Boussinesq fluid with infinite Prandtl number,
  at high Rayleigh numbers. With stress free boundary conditions
  and fixed heat flux on upper and lower boundaries, convection
  cells develop with aspect ratios (width/depth) λ≿ 5, if heat
  is supplied either entirely from within or entirely from below the
  fluid layer. The preferred aspect ratio is affected by the lateral
  boundary conditions. If the temperature, rather than the heat flux,
  is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh
  numbers of 2.4 × 10 <SUP>5</SUP> and greater, small sinking sheets
  are superimposed on the large aspect ratio cells, though they do not
  disrupt the circulation. Similar two-scale flows have been proposed
  for convection in the earth's mantle. The existence of two scales of
  flow in two-dimensional numerical experiments when the viscosity is
  constant will allow a variety of geophysically important effects to
  be investigated.

Title: Magnetic activity and variations in solar luminosity
Authors: Spiegel, E. A.; Weiss, N. O.
Bibcode: 1980Natur.287..616S
Altcode:
  Attempts to detect changes in the solar luminosity suggest that the
  solar constant has been misnamed<SUP>1-4</SUP>. Although the Nimbus
  satellite data<SUP>4</SUP> show no significant fractional variations
  above 5 × 10<SUP>-3</SUP> during the period 1975-78, results from
  recent balloon<SUP>5</SUP> and rocket<SUP>6</SUP> flights show changes
  of 4 × 10<SUP>-3</SUP>. Intense magnetic fields in sunspots hamper
  convection locally<SUP>7</SUP> but active regions are believed not
  to be directly responsible for long term variations in luminosity of
  the Sun<SUP>8</SUP> or of RS CVn and BY Dra stars<SUP>9</SUP>. The
  cause of luminosity variations over spot cycles should be sought
  in more deep-seated global features. Here we indicate how strong
  magnetic fields at the base of the convective zone can alter the local
  convection. The resulting changes in thermal energy are large enough
  to produce variations of order 0.1% in the solar luminosity over the
  11-yr sunspot cycle.

Title: Problems on Interior Structure, the Solar Dynamo and the Role
    of SCADM in Providing Interior Diagnostics
Authors: Weiss, N. O.
Bibcode: 1980NASCP2098...55W
Altcode: 1980sscs.nasa...55W
  What is already known about the structure of the Sun, the motion
  of its convective zone, and the solar cycle is reviewed. Topics
  discussed include solar variability, solar 'seismology', velocity
  patterns, magnetic fields, and the dynamo theory. Observations are
  needed to determine global properties (solar luminosity and radius),
  oscillations (p and g models), velocities (variation of rotation with
  time and depth), and magnetic fields.

Title: The nature of solar behaviour
Authors: Weiss, N. O.
Bibcode: 1980asfr.symp....1W
Altcode:
  Current knowledge of the present state of the sun and of its evolution
  since formation as a main sequence star 4.7 billion years ago is
  reviewed as an astrophysical background to studies of the fossil record
  of solar behavior. Attention is given to the internal structure of the
  sun as a reflection of the thermonuclear energy generation processes
  and convective energy dissipation processes occurring there, and to
  the magnetic fields caused by motions in the convective zone, which
  are responsible for solar activity. The long-term variability of the
  periodic changes in solar magnetic fields explained by kinematic
  dynamo theory is then considered in light of the sunspot record,
  terrestrial records, and the relationship between magnetic activity,
  solar luminosity and terrestrial climate. The evident magnetic
  properties of the sun are compared with those observed in other stars,
  and it is concluded that solar activity may have been 10 to 100 times
  more vigorous than at present when the sun reached the main sequence,
  and even more violent before then.

Title: Andrew Marvell and the Maunder Minimum
Authors: Weiss, J. E.; Weiss, N. O.
Bibcode: 1979QJRAS..20..115W
Altcode:
  No abstract at ADS

Title: Buoyant magnetic flux tubes in supergranules.
Authors: Meyer, F.; Schmidt, H. U.; Simon, G. W.; Weiss, N. O.
Bibcode: 1979A&A....76...35M
Altcode:
  The motion of filamentary flux tubes is described by a simplified
  model. Relative to the prescribed supergranular flow, the tubes drift at
  a rate determined by magnetic buoyancy, Lorentz forces and aerodynamic
  drag. The effect of buoyancy is most pronounced near the surface:
  small flux tubes are swept towards the network at the edge of a cell
  but those with larger fluxes float vertically at the center. New flux
  emerges at the center of the cell. These results are related to the
  emergence of active regions and ephemeral active regions, and to the
  slow decay of sunspots.

Title: The pattern of convection in the sun.
Authors: Weiss, N. O.
Bibcode: 1979psa..conf..121W
Altcode:
  No abstract at ADS

Title: The nature of solar behavior
Authors: Weiss, N. O.
Bibcode: 1979LPICo.390..106W
Altcode:
  No abstract at ADS

Title: Magnetic flux ropes and convection
Authors: Galloway, D. J.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1978JFM....87..243G
Altcode:
  Three-dimensional cellular convection concentrates magnetic flux into
  ropes when the magnetic Reynolds number is large. Amplification of
  the magnetic field is limited by the Lorentz force and the maximum
  field in a flux rope can be estimated. Boundary-layer analysis yields
  a completely self-consistent solution for a model of convection driven
  by imposed horizontal temperature gradients, and the transition from a
  kinematic to a dynamic regime can be followed in detail. The maximum
  value of the amplified field is proportional to the square root of
  the ratio of the viscous to the magnetic diffusivity.

Title: Small-scale magnetic fields and convection in the solar
    photosphere.
Authors: Weiss, N. O.
Bibcode: 1978MNRAS.183P..63W
Altcode:
  The detection of solar magnetic structures with diameters less
  than 300 km, as reported by Ramsey et al. (1977), is related to
  theoretical studies of the nonlinear interaction between magnetic
  fields and convection. In particular, it is shown that the location
  of the small-scale magnetic fields at the centers of granules cannot
  be readily explained on the basis of theoretical investigations of
  vigorous Boussinesq convection in a magnetic field.

Title: On the dynamic interaction between magnetic fields and
    convection.
Authors: Peckover, R. S.; Weiss, N. O.
Bibcode: 1978MNRAS.182..189P
Altcode:
  A simple two-dimensional model of convection in an electrically
  conducting Boussinesq fluid with an externally imposed magnetic field
  has been investigated in a series of numerical experiments. Convection
  is driven by horizontal gradients in an imposed temperature field
  which is unaffected by the motion. The transition from a kinematic to
  a dynamic regime is studied: magnetic flux is concentrated into ropes
  and the maximum field strength depends on the ratio of the viscous
  and magnetic diffusivities. The magnetic energy density in the ropes
  is unrelated to, and may be much greater than, the kinetic energy
  density outside. These results are relevant to the interaction between
  small-scale magnetic fields and photospheric granulation in the sun.

Title: The stability of sunspots.
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.
Bibcode: 1977MNRAS.179..741M
Altcode:
  The energy principle of Bernstein et al. (1958) is used to demonstrate
  that a magnetic flux tube in equilibrium with an external stratified
  field-free gas is stable to interchanges, provided the magnitude of the
  radial field component decreases upward on the tube boundary. Stability
  conditions on the external pressure in the case where a vacuum field is
  inside the flux tube are investigated, and it is found that both stable
  and unstable vacuum-field configurations can exist. A vacuum-field
  model is employed to show that tubes with fluxes greater than about
  10 to the 19th power Mx are stable in the sun, and this result is
  applied to observations of small-scale solar magnetic fields as well
  as to sunspot groups. Analysis of a simple sunspot model indicates
  that a sunspot can be stable in and immediately below the photosphere,
  that this stability is related to the potential energy associated with
  the Wilson depression, and that twisted fields need not be invoked.

Title: Formation of intense magnetic fields near the surface of
    the sun
Authors: Galloway, D. J.; Proctor, M. R. E.; Weiss, N. O.
Bibcode: 1977Natur.266..686G
Altcode:
  Possible mechanisms for the concentration of magnetic flux in the solar
  photosphere in the form of ropes of average magnetic field strengths
  of about 1500 gauss are discussed. Some upper limits to amplification
  of magnetic fields by convection are obtained on the assumption that
  the field strength cannot exceed the value for which the power needed
  to contain the flux rope is equal to the rate of turbulent energy
  dissipation. It is shown that the maximum field strength produced by
  flux concentration is typically an order of magnitude higher than the
  equipartition limit.

Title: Small scale solar magnetic fields: theory.
Authors: Weiss, N. O.
Bibcode: 1977IAUS...62..241W
Altcode:
  No abstract at ADS

Title: Numerical methods in convection theory
Authors: Weiss, N. O.
Bibcode: 1977LNP....71..142W
Altcode: 1977stco.coll..142W; 1977IAUCo..38..142W; 1977psc..conf..142W
  Nonlinear astrophysical convection is analyzed numerically, with
  attention to the relationship between convective heat transport and
  the super-adiabatic temperature gradient. Cellular patterns revealed
  by direct solar observations are modeled by two and three dimensional
  methods. The stability of the models is then evaluated on the basis
  of axisymmetric flow subjected to nonaxisymmetric perturbations.

Title: Magnetic fields and convection
Authors: Weiss, N. O.
Bibcode: 1977LNP....71..176W
Altcode: 1977IAUCo..38..176W; 1977stco.coll..176W; 1977psc..conf..176W
  In a highly conducting plasma convection is hindered by the imposition
  of a magnetic field. Convection may set in as direct or overstable modes
  and behavior near the onset of instability depends on the ratio of the
  magnetic to the thermal diffusivity. Vigorous convection produces local
  flux concentrations with magnetic fields that may be much greater than
  the equipartition value. The interaction between magnetic fields and
  convection can be observed in detail on the sun and is essential to
  any stellar dynamo.

Title: The calibration of stellar convection theories.
Authors: Gough, D. O.; Weiss, N. O.
Bibcode: 1976MNRAS.176..589G
Altcode:
  Any formula used to calculate the temperature gradient in a stellar
  convection zone must be calibrated, for example, by evolving
  1-solar-mass stellar models to fit the present age, luminosity, and
  effective temperature of the sun. When this procedure is followed
  for various convection theories, including those of Opik (1950)
  and Boehm-Vitense (1958), the corresponding models become almost
  indistinguishable. In particular, they predict the same depth, around
  150,000 km, for the solar convective zone.

Title: Convective Instability in a Compressible Atmosphere. II
Authors: Gough, D. O.; Moore, D. R.; Spiegel, E. A.; Weiss, N. O.
Bibcode: 1976ApJ...206..536G
Altcode:
  The onset of steady convection in polytropic atmosphere with constant
  viscosity is studied numencally. Subject headings: convection :
  atmospheres

Title: Magnetohydrodynamics (Book Review)
Authors: Mestel, L.; Weiss, N. O.
Bibcode: 1976ApL....17..152M
Altcode:
  No abstract at ADS

Title: The Solar Magnetic Field - Observation and Theory
Authors: Weiss, N. O.
Bibcode: 1976IAUTB..16..240W
Altcode: 1976IAUT...16B.240W
  No abstract at ADS

Title: Stability of sunspots
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.
Bibcode: 1976MitAG..40..160M
Altcode:
  No abstract at ADS

Title: The Pattern of Convection in the Sun
Authors: Weiss, N. O.
Bibcode: 1976IAUS...71..229W
Altcode:
  No abstract at ADS

Title: Axisymmetric convection in a cylinder
Authors: Jones, C. A.; Moore, D. R.; Weiss, N. O.
Bibcode: 1976JFM....73..353J
Altcode:
  The geometrical properties of axisymmetric convection in a Boussinesq
  fluid contained in a cylindrical cell with free boundaries
  are investigated. The range of unsteady behavior requiring a
  full three-dimensional solution of the governing equations is not
  considered. The solution near the critical Reynolds number is obtained
  from a perturbation expansion. For values of the Nusselt number not
  greater than 2, solutions are obtained from an expansion in a finite
  number of vertical modes. For Prandtl numbers less than unity the
  solution becomes independent of the Prandtl number at large Reynolds
  numbers. As the Prandtl number approaches 0 the Nusselt number is
  a function of the Rayleigh number only and there is an effective
  critical Rayleigh number equal to 1.32 times the critical Rayleigh
  number. Numerical results obtained for Rayleigh numbers up to 100 times
  the critical Rayleigh number and Prandtl numbers not in excess of 0.01
  are similar to those for two-dimensional rolls. For Prandtl numbers
  greater than unity there is a viscous regime. At high Rayleigh numbers
  a large isothermal region develops in which the ratio of vorticity to
  distance from the axis is almost constant.

Title: What drives the solar cycle?
Authors: Weiss, Nigel
Bibcode: 1975Natur.258..197W
Altcode:
  No abstract at ADS

Title: The growth and decay of sunspots.
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
Bibcode: 1974MNRAS.169...35M
Altcode:
  Sunspots are formed between supergranules, at junctions in the
  chromospheric network. Many spots disappear rapidly. However, some large
  spots enter a phase of slow decay: an annular cell develops, centered
  on the spot and with a systematic outward velocity directed from the
  penumbra toward the nearest faculae. This flow forms a moat around
  the spot swept clear of magnetic field except for magnetic features
  which migrate from the penumbra to the surrounding network. This
  phase may persist for several months before the spot is finally
  destroyed. Throughout this period the sunspot area, and hence its flux,
  decrease at a constant rate. The evolution of a sunspot is related
  to subphotospheric convection, with particular emphasis on a model of
  the slow decay phase which explains the steady decay of magnetic flux.

Title: A Theoretical Model for the Convection of Magnetic Flux in
    and Near Sunspots
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
Bibcode: 1974IAUS...56..235M
Altcode:
  No abstract at ADS

Title: Introduction to Magnetohydrodynamics
Authors: Weiss, N. O.
Bibcode: 1974magn.conf....2W
Altcode: 1974SAAS....4....2W
  Field in conducting fluids Maxwell's equations and the
  magnetohydrodynamic approximation Kinematic magnetohydrodynamics
  and the magnetic Reynolds number Perfectly conducting fluids
  Flux conservation: Alfvén's theorem Consequences of flux-freezing
  Hydromagnetic waves Alfvén waves Magneto-sonic waves Equilibria and
  stability Magnetohydrostatic equilibria Force-free fields The Virial
  theorem Stability problems Effects of finite resistivity Static
  diffusion Effects of motion Currents in ionized gases Fully ionized
  gas: two-fluid model Slightly ionized gas: three-fluid model Other
  dissipative processes References

Title: Convection in the earth's mantle: towards a numerical
    simulation
Authors: McKenzie, D. P.; Roberts, J. M.; Weiss, N. O.
Bibcode: 1974JFM....62..465M
Altcode:
  No abstract at ADS

Title: Dynamo Maintenance of Magnetic Fields in Stars
Authors: Weiss, N. O.
Bibcode: 1974magn.conf..185W
Altcode: 1974SAAS....4..185W
  Astrophysical magnetic fields Introduction Observed magnetic fields
  Hydromagnetic dynamos The solar cycle Observations Phenomenological
  model Kinematic dynamo theory Cowling's theorem Simple dynamo models
  Computational techniques Finite differences Expansion in toroidal
  and poloidal spherical harmonics Macroscopic dynamos Mean field
  electrodynamics The dynamo equations Mean field electrodynamics Dynamo
  models Constant α α<SUP>2</SUP> dynamos αω dynamos Oblique rotators
  Magnetohydrodynamic dynamos Mean field dynamos Macroscopic motions
  Convective models Dynamo action in the sun and stars Astrophysical
  dynamos Convection and magnetic fields in the sun Problems of the
  solar dynamo Stellar dynamos References

Title: Magnetohydrodynamics
Authors: Mestel, L.; Weiss, N. O.
Bibcode: 1974magn.conf.....M
Altcode: 1974mssa.book.....M; 1974QB353.M47......; 1974SAAS....4.....M
  No abstract at ADS

Title: Two-dimensional Rayleigh-Benard convection
Authors: Moore, D. R.; Weiss, N. O.
Bibcode: 1973JFM....58..289M
Altcode:
  No abstract at ADS

Title: The Dynamo Problem
Authors: Weiss, N. O.
Bibcode: 1971QJRAS..12..432W
Altcode:
  No abstract at ADS

Title: Theories of Large Scale Fields and the Magnetic Active Cycle
Authors: Weiss, N. O.
Bibcode: 1971IAUS...43..757W
Altcode:
  No abstract at ADS

Title: On the Magnetic Field in Pores
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1970SoPh...13...85S
Altcode:
  The magnetic field in an axisymmetric pore is current free and
  can be represented by a flux tube with a magnetic potential of the
  formAJ<SUB>0</SUB>(kr)e<SUP>-kz</SUP>. For a given magnetic flux the
  field in this pore model is uniquely defined if the magnetic pressure
  balances the gas pressure at two levels. For models with fluxes of
  0.5-3.0 × 10<SUP>20</SUP> mx the surface radius varies from 1100-2700
  km (diameters of 3-8 arc-sec) and the Wilson depression is estimated
  at 200 km. As the flux increases, the field becomes nearly horizontal
  at the edge of the pore and eventually a penumbra is formed. The
  distinction between pores and sunspots is investigated; the critical
  flux is about 10<SUP>20</SUP> Mx, corresponding to a radius of 1500 km.

Title: On the Magnetic Field in Pores
Authors: Weiss, N. O.; Simon, G. W.
Bibcode: 1969BAAS....1S.295W
Altcode:
  No abstract at ADS

Title: Sunspots and photospheric convection
Authors: Weiss, N. O.
Bibcode: 1969pia..conf..153W
Altcode:
  No abstract at ADS

Title: Supergranules and the Hydrogen Convection Zone
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1968ZA.....69..435S
Altcode:
  No abstract at ADS

Title: Supergranules and the Hydrogen Convection Zone.
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1968AJS....73S..77S
Altcode:
  The strong magnetic fields observed between supergranules indicate
  that there must be subphotospheric convection in cells with a
  preferred diameter of about 30 000 km. Orthodox mixing length theory
  assumes that the dimensions of cells are limited by the density scale
  height. This is adequate fot explaining granules but cannot account
  for supergranulation. A model is therefore proposed in which cellular
  motions extend over several scale heights. In addition to granules
  ~nd supergranules, this model predicts a third characteristic scale
  of motion, with giant cells around 300 000 km in diameter, These cells
  may produce a pattern of magnetic fields like that suggested by Bumba
  and Howard for complexes of activity.

Title: Concentration of Magnetic Fields in the Deep Convection Zone
Authors: Simon, G. W.; Weiss, N. O.
Bibcode: 1968IAUS...35..108S
Altcode:
  No abstract at ADS

Title: Convection in the Earth's mantle
Authors: Allan, D. W.; Thompson, W. B.; Weiss, N. O.
Bibcode: 1967metp.conf..507A
Altcode:
  No abstract at ADS

Title: Concentration of magnetic fields by convection in the Sun
Authors: Weiss, N. O.
Bibcode: 1967maco.conf..262W
Altcode:
  No abstract at ADS

Title: The Expulsion of Magnetic Flux by Eddies
Authors: Weiss, N. O.
Bibcode: 1966RSPSA.293..310W
Altcode: 1966RSLPS.293..310W
  A convective eddy imposed on an initially uniform magnetic field in a
  highly conducting fluid distorts the lines of force and amplifies the
  field. Flux is concentrated outside the eddy; within it, the field grows
  and its scale of variation decreases until resistive effects become
  important. Closed lines of force are then formed by reconnexion. The
  central field decays and a steady state is reached. Within a period,
  small compared with the characteristic time for resistive decay,
  magnetic flux is almost entirely expelled from regions of rapid motion
  and concentrated at the edges of convection cells. This process is
  demonstrated from numerical experiments. The results are applied to
  the sun, where the concentrated fields are strong enough to inhibit
  convection locally.

Title: Convection and the differential rotation of the Sun
Authors: Weiss, N. O.
Bibcode: 1965Obs....85...37W
Altcode:
  No abstract at ADS

Title: Magnetic flux tubes and convection in the sun
Authors: Weiss, N. O.
Bibcode: 1965IAUS...22..330W
Altcode:
  No abstract at ADS

Title: Convection in the Presence of Restraints
Authors: Weiss, N. O.
Bibcode: 1964RSPTA.256...99W
Altcode:
  In the presence of rotation or a magnetic field, the linearized
  convection problem reduces to a cubic characteristic equation. In part
  I, general methods are given for determining the onset of convection;
  in particular, the transition from oscillatory to steady modes is
  considered. The importance of this transition arises from evidence that
  oscillatory modes are inefficient at transporting heat. These methods
  are then applied to a rotating system where the critical Rayleigh
  number can be expressed in terms of a Taylor number. It is found that
  overstable modes develop into steady unstable modes before the exchange
  of stabilities for Prandtl numbers less than one-third. The nature
  of the motions is discussed and a similar treatment is provided for
  convection in a magnetic field. In part II, criteria for the onset
  of instability are derived from physical arguments. Convection can
  be treated by balancing the work done by buoyancy forces against the
  energy dissipated. In a rotating system, the effect of the Coriolis
  forces is to restrict the cell width and thus to enhance dissipation
  and promote stability. A magnetic field similarly attenuates the cells
  and prevents steady convection until the liberated kinetic energy
  exceeds the energy in the field. In part III, a cellular model is
  proposed for turbulent convection in a fluid of negligible viscosity,
  where the motion is limited by the non-linear transfer of energy to
  smaller-scale motions. If the Rayleigh number R<SUB>3</SUB> = gα β
  d<SUP>4</SUP>/π <SUP>4</SUP>kappa <SUP>2</SUP>&gt;&gt; 1 the convective
  transport varies as R<SUB>3</SUB><SUP>1/2</SUP>, while it varies as
  R<SUB>3</SUB><SUP>2</SUP> when R<SUB>3</SUB>&lt;&lt; 1. The discussion
  is extended to convection in the presence of rotation or a magnetic
  field; it is shown that overstable perturbations cannot develop into
  steady turbulent convection unless the system is already unstable to
  non-oscillatory modes. The transition from overstable to steady modes
  should therefore correspond to a sharp increase in convective transport.

Title: Magnetic flux tubes and convection in the Sun
Authors: Weiss, N. O.
Bibcode: 1964MNRAS.128..225W
Altcode:
  Convection in the Sun is apparently cellular and the convective
  velocities can be estimated. The interaction of cellular convection
  with a weak magnetic field leads to concentrated ropes of flux in the
  convective zone with fields of about 5000 gauss and fluxes of 1021
  maxwells in agreement with observation. These flux tubes tend to float
  outwards from the centre of the Sun. The magnetic pressure associated
  with the fields required to halt photospheric convection is comparable
  with the gas pressure and so fields will generally be diffuse as in
  bipolar magnetic regions. Occasionally the flux is concentrated to
  form a sunspot but the cooling is insignificant at more than 1000 km
  below the surface of the Sun.

Title: Nouvelles de la Science. - Varietes. La prochaine comete.
Authors: Weiss
Bibcode: 1886LAstr...5..109W
Altcode:
  No abstract at ADS

