140 research outputs found
Nonlinear dynamo in a short Taylor-Couette setup
It is numerically demonstrated by means of a magnetohydrodynamics code that a
short Taylor-Couette setup with a body force can sustain dynamo action. The
magnetic threshold is comparable to what is usually obtained in spherical
geometries. The linear dynamo is characterized by a rotating equatorial dipole.
The nonlinear regime is characterized by fluctuating kinetic and magnetic
energies and a tilted dipole whose axial component exhibits aperiodic reversals
during the time evolution. These numerical evidences of dynamo action in a
short Taylor-Couette setup may be useful for developing an experimental device
Electromagnetic induction in non-uniform domains
Kinematic simulations of the induction equation are carried out for different
setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material
properties of the flow driving impellers are considered by means of high
conducting and high permeability disks that are present in a cylindrical volume
filled with a conducting fluid. Two entirely different numerical codes are
mutually validated by showing quantitative agreement on Ohmic decay and
kinematic dynamo problems using various configurations and physical parameters.
Field geometry and growth rates are strongly modified by the material
properties of the disks even if the high permeability/high conductivity
material is localized within a quite thin region. In contrast the influence of
external boundary conditions remains small. Utilizing a VKS like mean fluid
flow and high permeability disks yields a reduction of the critical magnetic
Reynolds number for the onset of dynamo action of the simplest non-axisymmetric
field mode. However this decrease is not sufficient to become relevant in the
VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by
tiny changes in the flow configuration so that the result is not very robust
against small modifications of setup and properties of turbulence
Nonlinear dynamo action in a precessing cylindrical container
It is numerically demonstrated by means of a magnetohydrodynamics (MHD) code
that precession can trigger the dynamo effect in a cylindrical container. This
result adds credit to the hypothesis that precession can be strong enough to be
one of the sources of the dynamo action in some astrophysical bodies.Comment: 5 pages, 5 figures including subfigure
Full sphere hydrodynamic and dynamo benchmarks
Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamic behaviour of such systems. We report on the first community activity to compare numerical results of computer codes designed to calculate fluid flow within a whole sphere. The flows are incompressible and rapidly rotating and the forcing of the flow is either due to thermal convection or due to moving boundaries. All problems defined have solutions that allow easy comparison, since they are either steady, slowly drifting or perfectly periodic. The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for the flow. Benchmark 1 is purely hydrodynamic, and has a drifting solution. Benchmark 2 is a magnetohydrodynamic benchmark that can generate oscillatory, purely periodic, flows and magnetic fields. In contrast, Benchmark 3 is a hydrodynamic rotating bubble benchmark using no slip boundary conditions that has a stationary solution. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourierâfinite element code. There is good agreement between codes. It is found that in Benchmarks 1 and 2, the approximation of a whole sphere problem by a domain that is a spherical shell (a sphere possessing an inner core) does not represent an adequate approximation to the system, since the results differ from whole sphere results
A spherical shell numerical dynamo benchmark with pseudo vacuum magnetic boundary conditions
It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for driving the convection generate a fluid flow that is able to induce magnetic fields; numerous sophisticated computer codes are able to simulate the dynamic behaviour of such systems. This paper reports the results of a community activity aimed at comparing numerical results of several different types of computer codes that are capable of solving the equations of momentum transfer, magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core. The electrically conducting fluid is incompressible and rapidly rotating and the forcing of the flow is thermal convection under the Boussinesq approximation. We follow the original specifications and results reported in Harder & Hansen to construct a specific benchmark in which the boundaries of the fluid are taken to be impenetrable, non-slip and isothermal, with the added boundary condition for the magnetic field <b>B</b> that the field must be entirely radial there; this type of boundary condition for <b>B</b> is frequently referred to as âpseudo-vacuumâ. This latter condition should be compared with the more frequently used insulating boundary condition. This benchmark is so-defined in order that computer codes based on local methods, such as finite element, finite volume or finite differences, can handle the boundary condition with ease. The defined benchmark, governed by specific choices of the Roberts, magnetic Rossby, Rayleigh and Ekman numbers, possesses a simple solution that is steady in an azimuthally drifting frame of reference, thus allowing easy comparison among results. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement among codes
Direct numerical simulation of the axial dipolar dynamo in the Von KĂĄrmĂĄn Sodium experiment
For the first time, a direct numerical simulation of the incompressible, fully nonlinear, magnetohydrodynamic (MHD) equations for the Von KĂĄrmĂĄn Sodium (VKS) experiment is presented with the two counter-rotating impellers realistically represented. Dynamo thresholds are obtained for various magnetic permeabilities of the impellers and it is observed that the threshold decreases as the magnetic permeability increases. Hydrodynamic results compare well with experimental data in the same range of kinetic Reynolds numbers: at small impeller rotation frequency, the flow is steady; at larger frequency, the fluctuating flow is characterized by small scales and helical vortices localized between the blades. MHD computations show that two distinct magnetic families compete at small kinetic Reynolds number and these two families merge at larger kinetic Reynolds number. In both cases, using ferromagnetic material for the impellers decreases the dynamo threshold and enhances the axisymmetric component of the magnetic field: the resulting dynamo is a mostly axisymmetric axial dipole with an azimuthal component concentrated in the impellers as observed in the VKS experiment
Influence of high permeability disks in an axisymmetric model of the Cadarache dynamo experiment
Numerical simulations of the kinematic induction equation are performed on a
model configuration of the Cadarache von-K\'arm\'an-Sodium dynamo experiment.
The effect of a localized axisymmetric distribution of relative permeability
{\mu} that represents soft iron material within the conducting fluid flow is
investigated. The critical magnetic Reynolds number Rm^c for dynamo action of
the first non-axisymmetric mode roughly scales like
Rm^c({\mu})-Rm^c({\mu}->infinity) ~ {\mu}^(-1/2) i.e. the threshold decreases
as {\mu} increases. This scaling law suggests a skin effect mechanism in the
soft iron disks. More important with regard to the Cadarache dynamo experiment,
we observe a purely toroidal axisymmetric mode localized in the high
permeability disks which becomes dominant for large {\mu}. In this limit, the
toroidal mode is close to the onset of dynamo action with a (negative)
growth-rate that is rather independent of the magnetic Reynolds number. We
qualitatively explain this effect by paramagnetic pumping at the fluid/disk
interface and propose a simplified model that quantitatively reproduces
numerical results. The crucial role of the high permeability disks for the mode
selection in the Cadarache dynamo experiment cannot be inferred from
computations using idealized pseudo-vacuum boundary conditions (H x n = 0).Comment: 16 pages, 9 Figures, published in New Journal of Physics 14(2012),
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