Three-dimensional stability of a rotating MHD flow

The increase of quality of semi-conductors grown under rotating magnetic fields has recently motivated many numerical studies aiming at predicting the flow induced by the associated electromagnetic body forces in a finite length container filled with a liquid metal. The mean feature of the basic flow is now well known but the hydrodynamic stability of the solution is the subject of many researches which are conducted either experimentally or numerically. From these stability studies, it appears that the value of the critical magnetic Taylor number, Tm, which is deduced is a decreasing function of the aspect ratio H/R of the cylinder. Nevertheless, most of the numerical studies have assumed an axial symmetry of the flow. This problem is reconsidered here with a three-dimensional code. Surprisingly, it is found that no significant azimuthal modes develop for Taylor numbers up to twice the critical value. Even small, the non-axisymmetric modes are found to grow faster near the Ekman layers than in the core flow.