A. Tilgner

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.

Finite-amplitude convection in rotating spherical fluid shells

Finite-amplitude convection in rotating spherical fluid shells is considered for a variety of Prandtl numbers P and Rayleigh numbers Ra up to about 10 times the critical value. Convection at low Rayleigh numbers in the form of azimuthally periodic or weakly aperiodic drifting waves is characterized by relatively low heat transport, especially for P ≲ 1. The transition to strongly time-dependent convection leads to a rapid increase of the heat transport with increasing Rayleigh numbers. Onset of convection in the polar regions is delayed, but contributes a disproportionate fraction of the heat transport at high Rayleigh number. The differential rotation generated by convection, the distributions of helicity, and the role of asymmetry with respect to the equatorial plane are also studied.

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.

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.

Fluid flows in precessing spherical shells

Numerical solutions for fluid flows in precessing spherical cavities and spherical shells have been obtained and are compared with earlier analytical expressions. It is shown that the approximate validity of the analytical expressions extends further than could have been expected. The details of the flow structure exhibit significant departures, however, from the assumptions of the analytical theory. Standing waves are found in the case of sufficiently thin shells. Some results on instabilities of the basic flow are also discussed.

Magnetohydrodynamic flow in precessing spherical shells

Flow in a rapidly rotating, precessing spherical shell is studied with and without an applied magnetic dipole field in order to model the Earths core. The primary response of the fluid to precessional forcing is a solid body rotation about an axis other than the rotation axis of the shell. The orientation and energy of that flow is predicted well by an asymptotic theory. Ekman layers at the boundaries of the shell break down at critical latitudes and spawn internal shear layers. The limit of small precession rate is investigated in particular: at zero magnetic field, the strongest shear layers are inclined at 30° with respect to the rotation axis of the shell and erupt at 30° latitude from the inner core. When a magnetic dipole field with its dipole oriented along the rotation axis of the shell is applied, shear zones develop additional structure and change position and orientation. At an Elsasser number of 10, most flow structures tend to align with the rotation axis of the shell

Towards experimental fluid dynamos

Abstract An experimental demonstration of a magnetic field generated by the motion of liquid conductor is still lacking despite the central role of the dynamo effect in geophysics and astrophysics. Several experiments are presently being prepared which aim at building a homogeneous dynamo on a laboratory scale. The technical difficulties involved in building a dynamo preclude an experiment which replicates all aspects of the geodynamo and realizability is the prime concern in the experimental projects. The flows resulting from the different driving mechanisms which have been proposed are compared and the considerations entering the design of a dynamo experiment are presented.

Subharmonic Dynamo Action of Fluid Motions with Two-Dimensional Periodicity

Kinematic dynamos based on steady velocity fields with two-dimensional periodicity are analysed numerically. The velocity fields of the study by G. O. Roberts (1972) are used and the analysis is extended to the case when the spatial periodicity of the magnetic field differs from that of the velocity field not only in the homogeneous third direction. While the solutions of Roberts correspond to the most efficient dynamos in most cases, there are some cases in which spatially subharmonic dynamos are preferred.

Saturation Mechanism in a Model of the Karlsruhe Dynamo

The dynamo experiment in Karlsruhe (Busse et al., 1998) has been successful in generating a self sustained magnetic field (Stieglitz and Muller, 2000). The focus of theoretical investigations now shifts from the study of the conditions for the onset of dynamo action to the mechanisms responsible for saturation. One might suspect that due to the guiding mechanical structures present in this experiment, saturation simply happens in that the magnetic field grows until the Lorentz force reduces the volumetric flow rate to its critical value, without any significant change to the shape of the velocity field. Any pressure applied by the pumps in addition to the critical pressure would be balanced by the Lorentz force according to this scenario. Experimental observations show however that volumetric flow rates continue to increase as a function of the applied pressure even when a steady dynamo field is present, which indicates that the velocity profile inside individual spin generators changes in response to the magnetic field.