Dynamically consistent laminar dynamos

H. Fuchs - K.-H. Radler - M. Rheinhardt - M. Schuler

Astrophysikalisces Institut Potsdam, An der Sternwarte 16, D-14482

Abstract
The paper presents some results of numerical simulations of a simple spherical laminar dynamo model. Both a kinematics version as well as some dynamically consistent version were studied. The model is defined by a spherical body of an electrically conducting incompressible fluid in non-conducting surroundings. In the kinematics approach the fluid motion is steady and symmetric about an axis and about the corresponding equatorial plane, and it satisfies the no-slip condition at the boundary. The critical magnetic Reynolds number and the corresponding magnetic field were calculated. For the dynamically consistent model a body force was introduced which just balances the inertial and viscous forces for the fluid motion considered in the kinematics case. At first studies of the fluid behaviour in the absence of Coriolis and Lorentz forces have been carried out. They revealed that the state with this motion is stable only in a certain range of the relevant parameters. Outside this range an evolution to other steady or even oscillatory states has been observed. In a number of simulations the full interaction between fluid motion and magnetic field was taken into account. In addition, in some cases also Coriolis forces were included. In several cases states with steady motions and magnetic fields were reached, in other cases the magnetic fields died out despite rather large magnetic Reynolds numbers. Figs 3, refs. 5.