733 research outputs found
Dipole Collapse and Dynamo Waves in Global Direct Numerical Simulations
Magnetic fields of low-mass stars and planets are thought to originate from
self-excited dynamo action in their convective interiors. Observations reveal a
variety of field topologies ranging from large-scale, axial dipole to more
structured magnetic fields. In this article, we investigate more than 70
three-dimensional, self-consistent dynamo models obtained by direct numerical
simulations. The control parameters, the aspect ratio and the mechanical
boundary conditions have been varied to build up this sample of models. Both,
strongly dipolar and multipolar models have been obtained. We show that these
dynamo regimes can in general be distinguished by the ratio of a typical
convective length scale to the Rossby radius. Models with a predominantly
dipolar magnetic field were obtained, if the convective length scale is at
least an order of magnitude larger than the Rossby radius. Moreover, we
highlight the role of the strong shear associated with the geostrophic zonal
flow for models with stress-free boundary conditions. In this case, the above
transition disappears and is replaced by a region of bistability for which
dipolar and multipolar dynamos co-exist. We interpret our results in terms of
dynamo eigenmodes using the so-called test-field method. We can thus show that
models in the dipolar regime are characterized by an isolated 'single mode'.
Competing overtones become significant as the boundary to multipolar dynamos is
approached. We discuss how these findings relate to previous models and to
observations.Comment: 35 pages, 16 figure
Mechanisms of Planetary and Stellar Dynamos
We review some of the recent progress on modeling planetary and stellar
dynamos. Particular attention is given to the dynamo mechanisms and the
resulting properties of the field. We present direct numerical simulations
using a simple Boussinesq model. These simulations are interpreted using the
classical mean-field formalism. We investigate the transition from steady
dipolar to multipolar dynamo waves solutions varying different control
parameters, and discuss the relevance to stellar magnetic fields. We show that
owing to the role of the strong zonal flow, this transition is hysteretic. In
the presence of stress-free boundary conditions, the bistability extends over a
wide range of parameters.Comment: Proceedings of IAUS 294 "Solar and Astrophysical Dynamos and Magnetic
Activity" Editors A.G. Kosovichev, E.M. de Gouveia Dal Pino, & Y.Yan,
Cambridge University Press, to appear (2013
The Magnetic Sun: Reversals and Long-Term Variations
A didactic introduction to current thinking on some aspects of the solar
dynamo is given for geophysicists and planetary scientists.Comment: 17 pages, 9 figures; Space Science Rev., in pres
Weak turbulence theory for rotating magnetohydrodynamics and planetary dynamos
A weak turbulence theory is derived for magnetohydrodynamics under rapid
rotation and in the presence of a large-scale magnetic field. The angular
velocity is assumed to be uniform and parallel to the constant
Alfv\'en speed . Such a system exhibits left and right circularly
polarized waves which can be obtained by introducing the magneto-inertial
length . In the large-scale limit (; being
the wave number), the left- and right-handed waves tend respectively to the
inertial and magnetostrophic waves whereas in the small-scale limit () pure Alfv\'en waves are recovered. By using a complex helicity
decomposition, the asymptotic weak turbulence equations are derived which
describe the long-time behavior of weakly dispersive interacting waves {\it
via} three-wave interaction processes. It is shown that the nonlinear dynamics
is mainly anisotropic with a stronger transfer perpendicular () than
parallel () to the rotating axis. The general theory may converge to
pure weak inertial/magnetostrophic or Alfv\'en wave turbulence when the large
or small-scales limits are taken respectively. Inertial wave turbulence is
asymptotically dominated by the kinetic energy/helicity whereas the
magnetostrophic wave turbulence is dominated by the magnetic energy/helicity.
For both regimes a family of exact solutions are found for the spectra which do
not correspond necessarily to a maximal helicity state. It is shown that the
hybrid helicity exhibits a cascade whose direction may vary according to the
scale at which the helicity flux is injected with an inverse cascade if
and a direct cascade otherwise. The theory is relevant for the
magnetostrophic dynamo whose main applications are the Earth and giant planets
for which a small () Rossby number is expected.Comment: 4 figures, 33 page
Magnetic Cycles in a Convective Dynamo Simulation of a Young Solar-type Star
Young solar-type stars rotate rapidly and many are magnetically active; some
undergo magnetic cycles similar to the 22-year solar activity cycle. We conduct
simulations of dynamo action in rapidly rotating suns with the 3D MHD anelastic
spherical harmonic (ASH) code to explore dynamo action achieved in the
convective envelope of a solar-type star rotating at 5 times the current solar
rotation rate. Striking global-scale magnetic wreaths appear in the midst of
the turbulent convection zone and show rich time-dependence. The dynamo
exhibits cyclic activity and undergoes quasi-periodic polarity reversals where
both the global-scale poloidal and toroidal fields change in sense on a roughly
1500 day time scale. These magnetic activity patterns emerge spontaneously from
the turbulent flow and are more organized temporally and spatially than those
realized in our previous simulations of the solar dynamo. We assess in detail
the competing processes of magnetic field creation and destruction within our
simulations that contribute to the global-scale reversals. We find that the
mean toroidal fields are built primarily through an -effect, while the
mean poloidal fields are built by turbulent correlations which are not
necessarily well represented by a simple -effect. During a reversal the
magnetic wreaths propagate towards the polar regions, and this appears to arise
from a poleward propagating dynamo wave. The primary response in the convective
flows involves the axisymmetric differential rotation which shows variations
associated with the poleward propagating magnetic wreaths. In the Sun, similar
patterns are observed in the poleward branch of the torsional oscillations, and
these may represent poleward propagating magnetic fields deep below the solar
surface. [abridged]Comment: 20 pages, 14 figures, emulateapj format; accepted for publication in
ApJ. Expanded and published version of sections 5-6 from
http://arxiv.org/abs/0906.240
Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere
Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations
are reported for the interior of a rotating, perfectly-conducting, rigid
spherical shell that is insulator-coated on the inside. A previously-reported
spectral method is used which relies on a Galerkin expansion in
Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in
this set of computations is the rigid rotation of the sphere. After a few
purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial
waves), attention is focused on selective decay and the MHD dynamo problem. In
dynamo runs, prescribed mechanical forcing excites a persistent velocity field,
usually turbulent at modest Reynolds numbers, which in turn amplifies a small
seed magnetic field that is introduced. A wide variety of dynamo activity is
observed, all at unit magnetic Prandtl number. The code lacks the resolution to
probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn
out to be plentiful in those parts of parameter space in which the code is
accurate. The key control parameters seem to be mechanical and magnetic
Reynolds numbers, the Rossby and Ekman numbers (which in our computations are
varied mostly by varying the rate of rotation of the sphere) and the amount of
mechanical helicity injected. Magnetic energy levels and magnetic dipole
behavior are exhibited which fluctuate strongly on a time scale of a few eddy
turnover times. These seem to stabilize as the rotation rate is increased until
the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic
Self-similarity of the dipole-multipole transition in rapidly rotating dynamos
The dipole-multipole transition in rapidly rotating dynamos is investigated
through the analysis of forced magnetohydrodynamic waves in an unstably
stratified fluid. The focus of this study is on the inertia-free limit
applicable to planetary cores, where the Rossby number is small not only on the
core depth but also on the length scale of columnar convection. By
progressively increasing the buoyant forcing in a linear magnetoconvection
model, the slow Magnetic-Archimedean-Coriolis (MAC) waves are significantly
attenuated so that their kinetic helicity decreases to zero; the fast MAC wave
helicity, on the other hand, is practically unaffected. In turn, polarity
reversals in low-inertia spherical dynamos are shown to occur when the slow MAC
waves disappear under strong forcing. Two dynamically similar regimes are
identified -- the suppression of slow waves in a strongly forced dynamo and the
excitation of slow waves in a moderately forced dynamo starting from a small
seed field. While the former regime results in polarity reversals, the latter
regime produces the axial dipole from a chaotic multipolar state. For either
polarity transition, a local Rayleigh number based on the mean wavenumber of
the energy-containing scales bears the same linear relationship with the square
of the peak magnetic field measured at the transition. The self-similarity of
the dipole-multipole transition can place a constraint on the Rayleigh number
for polarity reversals in the Earth.Comment: 31 pages, 18 figures, 3 table
Global magnetic cycles in rapidly rotating younger suns
Observations of sun-like stars rotating faster than our current sun tend to
exhibit increased magnetic activity as well as magnetic cycles spanning
multiple years. Using global simulations in spherical shells to study the
coupling of large-scale convection, rotation, and magnetism in a younger sun,
we have probed effects of rotation on stellar dynamos and the nature of
magnetic cycles. Major 3-D MHD simulations carried out at three times the
current solar rotation rate reveal hydromagnetic dynamo action that yields
wreaths of strong toroidal magnetic field at low latitudes, often with opposite
polarity in the two hemispheres. Our recent simulations have explored behavior
in systems with considerably lower diffusivities, achieved with sub-grid scale
models including a dynamic Smagorinsky treatment of unresolved turbulence. The
lower diffusion promotes the generation of magnetic wreaths that undergo
prominent temporal variations in field strength, exhibiting global magnetic
cycles that involve polarity reversals. In our least diffusive simulation, we
find that magnetic buoyancy coupled with advection by convective giant cells
can lead to the rise of coherent loops of magnetic field toward the top of the
simulated domain.Comment: 4 pages, 3 figures, from IAU 273: The Physics of Sun and Star Spot
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