128 research outputs found
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
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
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
Stability problem in dynamo
It is shown, that the saturated -effect taken from the nonlinear
dynamo equations for the thin disk can still produce exponentially growing
magnetic field in the case, when this field does not feed back on the .
For negative dynamo number (stationary regime) stability is defined by the
structure of the spectra of the linear problem for the positive dynamo numbers.
Stability condition for the oscillatory solution (positive dynamo number) is
also obtained and related to the phase shift of the original magnetic field,
which produced saturated and magnetic field in the kinematic regime.
Results can be used for explanation of the similar effect observed in the shell
models simulations as well in the 3D dynamo models in the plane layer and
sphere
Alpha effect due to buoyancy instability of a magnetic layer
A strong toroidal field can exist in form of a magnetic layer in the
overshoot region below the solar convection zone. This motivates a more
detailed study of the magnetic buoyancy instability with rotation. We calculate
the alpha effect due to helical motions caused by a disintegrating magnetic
layer in a rotating density-stratified system with angular velocity Omega
making an angle theta with the vertical. We also study the dependence of the
alpha effect on theta and the strength of the initial magnetic field. We carry
out three-dimensional hydromagnetic simulations in Cartesian geometry. A
turbulent EMF due to the correlations of the small scale velocity and magnetic
field is generated. We use the test-field method to calculate the transport
coefficients of the inhomogeneous turbulence produced by the layer. We show
that the growth rate of the instability and the twist of the magnetic field
vary monotonically with the ratio of thermal conductivity to magnetic
diffusivity. The resulting alpha effect is inhomogeneous and increases with the
strength of the initial magnetic field. It is thus an example of an
"anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around
8--16 Fourier modes to reconstruct the actual EMF based on the actual mean
field.Comment: 14 pages, 19 figures 3 tables (submitted to A & A
Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
A comparison is made between mean-field models and direct numerical
simulations of rotating magnetoconvection and the geodynamo. The mean-field
coefficients are calculated with the fluid velocity taken from the direct
numerical simulations. The magnetic fields resulting from mean-field models are
then compared with the mean magnetic field from the direct numerical
simulations
The fratricide of alpha-Omega dynamos by their alpha-squared siblings
Context. Helically forced magneto-hydrodynamic shearing-sheet turbulence can
support different large-scale dynamo modes, although the {\alpha} - {\Omega}
mode is generally expected to dominate because it is the fastest growing. In an
{\alpha} - {\Omega} dynamo, most of the field amplification is produced by the
shear. As differential rotation is an ubiquitous source of shear in
astrophysics, such dynamos are believed to be the source of most astrophysical
large-scale magnetic fields. Aims. We study the stability of oscillatory
migratory {\alpha} - {\Omega} type dynamos in turbulence simulations. Methods.
We use shearing-sheet simulations of hydromagnetic turbulence that is helically
forced at a wavenumber that is about three times larger than the lowest
wavenumber in the domain so that both {\alpha} - {\Omega} and {\alpha}2 dynamo
action is possible. Results. After initial dominance and saturation, the
{\alpha} - {\Omega} mode is found to be destroyed by an orthogonal {\alpha}2
mode sustained by the helical turbulence alone. We show that there are at least
two processes through which this transition can occur. Conclusions. The
fratricide of {\alpha} - {\Omega} dynamos by its {\alpha}2 sibling is discussed
in the context of grand minima of solar and stellar activity. However, the
genesis of {\alpha} - {\Omega} dynamos from an {\alpha}2 dynamo has not yet
been found.Comment: 10 pages, 12 figures, 3 table
Kinematic alpha effect in isotropic turbulence simulations
Using numerical simulations at moderate magnetic Reynolds numbers up to 220
it is shown that in the kinematic regime, isotropic helical turbulence leads to
an alpha effect and a turbulent diffusivity whose values are independent of the
magnetic Reynolds number, \Rm, provided \Rm exceeds unity. These turbulent
coefficients are also consistent with expectations from the first order
smoothing approximation. For small values of \Rm, alpha and turbulent
diffusivity are proportional to \Rm. Over finite time intervals meaningful
values of alpha and turbulent diffusivity can be obtained even when there is
small-scale dynamo action that produces strong magnetic fluctuations. This
suggests that small-scale dynamo-generated fields do not make a correlated
contribution to the mean electromotive force.Comment: Accepted for publication in MNRAS Letter
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