E. Grote

A numerical dynamo benchmark

We present the results of a benchmark study for a convection-driven magnetohydrodynamic dynamo problem in a rotating spherical shell. The solutions are stationary aside from azimuthal drift. One case of non-magnetic convection and two dynamos that differ in the assumptions concerning the inner core are studied. Six groups contributed numerical solutions which show good agreement. This provides an accurate reference standard with high confidence.

Regular and chaotic spherical dynamos

Abstract The generation of magnetic fields by thermal convection in rotating spherical shells has been simulated numerically in the case of Prandtl numbers of the order unity and Taylor numbers of the order 108. Regular and chaotic dipolar dynamos, hemispherical dynamos and quadrupolar dynamos have been found in different regions of the parameter space depending mainly on the magnetic Prandtl number Pm. The important role played by relaxation oscillations of the convection field is emphasized.

Dynamics of convection and dynamos in rotating spherical fluid shells

Numerical simulations of thermal convection in rapidly rotating spherical fluid shells have been carried out with and without magnetic fields generated by the dynamo process. Relaxation oscillations and localized convection activity represent coherent phenomena of turbulent convection in the absence of magnetic fields. In the presence of the latter, the coherent structures are destroyed and the heat transport is enhanced. With increasing Rayleigh number the magnetic energy tends to saturate and the magnetic field assumes an increasingly filamentary structure.

On Convection Driven Dynamos in Rotating Spherical Shells

Solutions for chaotic dynamos driven by thermal convection in a rotating spherical shell are obtained numerically for different Prandtl numbers. The influence of this parameter which is usually suppressed in the magnetostrophic approximation is emphasized in the present analysis.

Effects of hyperdiffusivities on dynamo simulations

A comparison of stationary and time periodic convection driven spherical dynamos computed with and without the use of hyperdiffusivities is presented.

Buoyancy Driven Convection in Rotating Spherical Shells and Its Dynamo Action

Scientific results based on computations carried out at the Stuttgart Supercomputing Center are presented. Coherent structures in turbulent convection are found and the form of magnetic fields generated by the dynamo action has been determined as a function of the parameters of the problem. The saturation of magnetic energy in dependence on the Rayleigh number is studied in a particular case.

Computations of Convection Driven Spherical Dynamos

The geodynamo, i.e. the process by which the Earth’s magnetic field is generated in the liquid outer core of the Earth, is generally regarded as one of the fundamental problems of geophysics. It is the prevailing opinion among geophysicists that thermal and chemical buoyancy originating in connection with the solidification of the inner core and the general cooling of the Earth cause convection flows in the outer core which consists of liquid iron together with some lighter elements. The mechanical energy of the convection flow provides the energy for the sustenance of the magnetic field against Ohmic losses. The mechanism by which this transfer of energy is accomplished is called a homogeneous dynamo in order to distinguish it from the common inhomogeneous dynamos used in technical applications.

Dynamics of Convection and Dynamos in Rotating Spheres

Large scale computer simulations of thermal convection in rapidly rotating spheres have been carried out with and without magnetic fields generated by the dynamo process. Relaxation oscillations and localized convection activity represent coherent phenomena of turbulent convection in the absence of magnetic fields. In the presence of the latter the coherent structures are destroyed and the heat transport is enhanced. A tendency towards saturation of the magnetic energy with increasing Rayleigh number has also been found.