343 research outputs found
Rotational threshold in global numerical dynamo simulations
Magnetic field observations of low-mass stars reveal an increase of magnetic
activity with increasing rotation rate. The so-called activity-rotation
relation is usually attributed to changes in the underlying dynamo processes
generating the magnetic field. We examine the dependence of the field strength
on rotation in global numerical dynamo models and interpret our results on the
basis of energy considerations. In agreement with the scaling law proposed by
Christensen & Aubert (2006), the field strength in our simulations is set by
the fraction of the available power used for the magnetic field generation.
This is controlled by the dynamo efficiency calculated as the ratio of Ohmic to
total dissipation in our models. The dynamo efficiency grows strongly with
increasing rotation rate at a Rossby number of 0.1 until it reaches its upper
bound of one and becomes independent of rotation. This gain in efficiency is
related to the strong rotational dependence of the mean electromotive force in
this parameter regime. For multipolar models at Rossby numbers clearly larger
than 0.1, on the other hand, we do not find a systematic dependence of the
field strength on rotation. Whether the enhancement of the dynamo efficiency
found in our dipolar models explains the observed activity-rotation relation
needs to be further assessed.Comment: 6 pages, 4 figure
Mode analysis of numerical geodynamo models
It has been suggested in Hoyng (2009) that dynamo action can be analysed by
expansion of the magnetic field into dynamo modes and statistical evaluation of
the mode coefficients. We here validate this method by analysing a numerical
geodynamo model and comparing the numerically derived mean mode coefficients
with the theoretical predictions. The model belongs to the class of
kinematically stable dynamos with a dominating axisymmetric, antisymmetric with
respect to the equator and non-periodic fundamental dynamo mode. The analysis
requires a number of steps: the computation of the so-called dynamo
coefficients, the derivation of the temporally and azimuthally averaged dynamo
eigenmodes and the decomposition of the magnetic field of the numerical
geodynamo model into the eigenmodes. For the determination of the theoretical
mode excitation levels the turbulent velocity field needs to be projected on
the dynamo eigenmodes. We compare the theoretically and numerically derived
mean mode coefficients and find reasonably good agreement for most of the
modes. Some deviation might be attributable to the approximation involved in
the theory. Since the dynamo eigenmodes are not self-adjoint a spectral
interpretation of the eigenmodes is not possible
Global dynamo models from direct numerical simulations and their mean-field counterparts
Context. The recently developed test-field method permits to compute dynamo
coefficients from global, direct numerical simulations. The subsequent use of
these parameters in mean-field models enables us to compare self-consistent
dynamo models with their mean-field counterparts. So far, this has been done
for a simulation of rotating magnetoconvection and a simple benchmark dynamo,
which are both (quasi-)stationary. Aims. It is shown that chaotically
time-dependent dynamos in a low Rossby number regime may be appropriately
described by corresponding mean-field results. Also, it is pointed out under
which conditions mean-field models do not match direct numerical simulations.
Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating,
spherical shell in the Boussinesq approximation. Based on this, we compute
mean-field coefficients for several models with the help of the previously
developed test-field method. The parameterization of the mean electromotive
force by these coefficients is tested against direct numerical simulations. In
addition, we use the determined dynamo coefficients in mean-field models and
compare the outcome with azimuthally averaged fields from direct numerical
simulations. Results. The azimuthally and time-averaged electromotive force in
fast rotating dynamos is sufficiently well parameterized by the set of
determined mean-field coefficients. In comparison to the previously considered
(quasi-)stationary dynamo, the chaotic time-dependence leads to an improved
scale separation and thus to a better agreement between direct numerical
simulations and mean-field results.Comment: 6 pages, 6 figure
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
Topology and field strength in spherical, anelastic dynamo simulations
Numerical modelling of convection driven dynamos in the Boussinesq
approximation revealed fundamental characteristics of the dynamo-generated
magnetic fields and the fluid flow. Because these results were obtained for an
incompressible fluid, their validity for gas planets and stars remains to be
assessed. A common approach is to take some density stratification into account
with the so-called anelastic approximation. The validity of previous results
obtained in the Boussinesq approximation is tested for anelastic models. We
point out and explain specific differences between both types of models, in
particular with respect to the field geometry and the field strength, but we
also compare scaling laws for the velocity amplitude, the magnetic dissipation
time, and the convective heat flux. Our investigation is based on a systematic
parameter study of spherical dynamo models in the anelastic approximation. We
make use of a recently developed numerical solver and provide results for the
test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and
multipolar dynamos identified in Boussinesq simulations is also present in our
sample of anelastic models. Dipolar models require that the typical length
scale of convection is an order of magnitude larger than the Rossby radius.
However, the distinction between both classes of models is somewhat less
explicit than in previous studies. This is mainly due to two reasons: we found
a number of models with a considerable equatorial dipole contribution and an
intermediate overall dipole field strength. Furthermore, a large density
stratification may hamper the generation of dipole dominated magnetic fields.
Previously proposed scaling laws, such as those for the field strength, are
similarly applicable to anelastic models. It is not clear, however, if this
consistency necessarily implies similar dynamo processes in both settings.Comment: 14 pages, 11 figure
Die Besteuerung von AlterseinkĂĽnften und des Altersvorsorgesparens
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Saturation and time dependence of geodynamo models
In this study we address the question under which conditions a saturated
velocity field stemming from geodynamo simulations leads to an exponential
growth of the magnetic field in a corresponding kinematic calculation. We
perform global self-consistent geodynamo simulations and calculate the
evolution of a kinematically advanced tracer field. The self-consistent
velocity field enters the induction equation in each time step, but the tracer
field does not contribute to the Lorentz force. This experiment has been
performed by Cattaneo & Tobias (2009) and is closely related to the test field
method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which
the tracer field either grows exponentially or approaches a state aligned with
the actual self-consistent magnetic field after an initial transition period.
Both regimes can be distinguished by the Rossby number and coincide with the
dipolar and multipolar dynamo regimes identified by Christensen & Aubert
(2006). Dipolar dynamos with low Rossby number are kinematically stable whereas
the tracer field grows exponentially in the multipolar dynamo regime. This
difference in the saturation process for dynamos in both regimes comes along
with differences in their time variability. Within our sample of 20 models,
solely kinematically unstable dynamos show dipole reversals and large
excursions. The complicated time behaviour of these dynamos presumably relates
to the alternating growth of several competing dynamo modes. On the other hand,
dynamos in the low Rossby number regime exhibit a rather simple time dependence
and their saturation merely results in a fluctuation of the fundamental dynamo
mode about its critical state.Comment: 6 pages, 8 figure
Oscillatory dynamos and their induction mechanisms
Context: Large-scale magnetic fields resulting from hydromagnetic dynamo
action may differ substantially in their time dependence. Cyclic field
variations, characteristic for the solar magnetic field, are often explained by
an important omega-effect, i.e. by the stretching of field lines due to strong
differential rotation. Aims: The dynamo mechanism of a convective, oscillatory
dynamo model is investigated. Methods: We solve the MHD-equations for a
conducting Boussinesq fluid in a rotating spherical shell. For a resulting
oscillatory model, dynamo coefficients have been computed with the help of the
so-called test-field method. Subsequently, these coefficients have been used in
a mean-field calculation in order to explore the underlying dynamo mechanism.
Results: Although the rather strong differential rotation present in this model
influences the magnetic field, the omega-effect alone is not responsible for
its cyclic time variation. If the omega-effect is suppressed, the resulting
alpha^2-dynamo remains oscillatory. Surprisingly, the corresponding alpha-omega
dynamo leads to a non-oscillatory magnetic field. Conclusions: The assumption
of an alpha-omega mechanism does not explain the occurrence of magnetic cycles
satisfactorily
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