Asymptotic flows in non uniform magnetic fields

T. Alboussiere¹ - J. P. Garandet² - R. Moreau¹

¹ Laboratoire EPM-Madylam, CNRS UPR A 9033, ENSHMG, BP 95, 38402, St. Martin d Heres Cedex, France
² Commissariat a l Energie Atomique DTA/CEREM/DEM/SES, Centre d Etudes Nucleares de Grenoble, 17 avenue des Martyrs, 38054 Grenoble Cedex 09, France

Abstract
For any given non uniform magnetic field and non electromagnetic driving force, an asymptotic analysis of the flow is performed using a curvilinear system of coordinates adapted to the magnetic field. This analysis yields the structure of the electric current density and velocity fields. Then, orthogonal planar symmetries are considered; a very significant simplification of the asymptotic structure is seen to take place depending on the nature of the symmetry. The asymptotic solution is explicitly derived for some configurations like fluid flow during crystal growth from the melt. In the case of electrically insulating boundaries, the nature of the symmetry is found to govern the magnitude and structure of the damped velocity. Figs 3, refs 8.