4,264 research outputs found
Predictive Scaling Laws for Spherical Rotating Dynamos
State of the art numerical models of the Geodynamo are still performed in a
parameter regime extremely remote from the values relevant to the physics of
the Earth's core. In order to establish a connection between dynamo modeling
and the geophysical motivation, {it is necessary to use} scaling laws. Such
scaling laws establish the dependence of essential quantities (such as the
magnetic field strength) on measured or controlled quantities. They allow for a
direct confrontation of advanced models with geophysical {constraints}.
(...)
We show that previous empirical scaling laws for the magnetic field strength
essentially reflect the statistical balance between energy production and
dissipation for saturated dynamos. Such power based scaling laws are thus
necessarily valid for any dynamo in statistical equilibrium and applicable to
any numerical model, irrespectively of the dynamo mechanism.
We show that direct numerical fits can provide contradictory results owing to
biases in the parameters space covered in the numerics and to the role of a
priori hypothesis on the fraction of ohmic dissipation.
We introduce predictive scaling laws, i.e. relations involving input
parameters of the governing equations only. We guide our reasoning on physical
considerations. We show that our predictive scaling laws can properly describe
the numerical database and reflect the dominant forces balance at work in these
numerical simulations. We highlight the dependence of the magnetic field
strength on the rotation rate. Finally, our results stress that available
numerical models operate in a viscous dynamical regime, which is not relevant
to the Earth's core
Asymptotic Solutions for Mean-Field Slab Dynamos
We discuss asymptotic solutions of the kinematic -dynamo in a
thin disc (slab). Focusing upon the strong dynamo regime, in which the dynamo
number satisfies , we resolve uncertainties in the earlier
treatments and conclude that some of the simplifications that have been made in
previous studies are questionable. Comparing numerical solutions with
asymptotic results obtained for and we find that the
asymptotic solutions give a reasonably accurate description of the dynamo even
far beyond their formal ranges of applicability. Indeed, our results suggest a
simple analytical expression for the growth rate of the mean magnetic field
that remains accurate in the range (which is appropriate for
dynamos in spiral galaxies and accretion discs). Finally, we analyse the role
of various terms in the dynamo equations to clarify the fine details of the
dynamo process.Comment: "This is an Author's Original Manuscript of an article submitted for
consideration in Geophysical and Astrophysical Fluid Dynamics [copyright
Taylor & Francis]; Geophysical and Astrophysical Fluid Dynamics is available
online at http://www.tandfonline.com/gafd
Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
Several recent advances in turbulent dynamo theory are reviewed. High
resolution simulations of small-scale and large-scale dynamo action in periodic
domains are compared with each other and contrasted with similar results at low
magnetic Prandtl numbers. It is argued that all the different cases show
similarities at intermediate length scales. On the other hand, in the presence
of helicity of the turbulence, power develops on large scales, which is not
present in non-helical small-scale turbulent dynamos. At small length scales,
differences occur in connection with the dissipation cutoff scales associated
with the respective value of the magnetic Prandtl number. These differences are
found to be independent of whether or not there is large-scale dynamo action.
However, large-scale dynamos in homogeneous systems are shown to suffer from
resistive slow-down even at intermediate length scales. The results from
simulations are connected to mean field theory and its applications. Recent
work on helicity fluxes to alleviate large-scale dynamo quenching, shear
dynamos, nonlocal effects and magnetic structures from strong density
stratification are highlighted. Several insights which arise from analytic
considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue
"Magnetism in the Universe" (ed. A. Balogh
The Integral Equation Method for a Steady Kinematic Dynamo Problem
With only a few exceptions, the numerical simulation of cosmic and laboratory
hydromagnetic dynamos has been carried out in the framework of the differential
equation method. However, the integral equation method is known to provide
robust and accurate tools for the numerical solution of many problems in other
fields of physics. The paper is intended to facilitate the use of integral
equation solvers in dynamo theory. In concrete, the integral equation method is
employed to solve the eigenvalue problem for a hydromagnetic dynamo model with
a spherically symmetric, isotropic helical turbulence parameter alpha. Three
examples of the function alpha(r) with steady and oscillatory solutions are
considered. A convergence rate proportional to the inverse squared of the
number of grid points is achieved. Based on this method, a convergence
accelerating strategy is developed and the convergence rate is improved
remarkably. Typically, quite accurate results can be obtained with a few tens
of grid points. In order to demonstrate its suitability for the treatment of
dynamos in other than spherical domains, the method is also applied to alpha^2
dynamos in rectangular boxes. The magnetic fields and the electric potentials
for the first eigenvalues are visualized.Comment: 22 pages, 18 figures, to appear in J. Comp. Phy
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