Variational principles and stability criteria for two-dimensional, gravitating, ideal magnetohydrodynamic configurations
Faculty of Sciences. Physics
Il Nuovo cimento della societÓ italiana di fisica : B: General physics, relativity, astronomy and mathematical physics and methods. - -, 1985 - 2008
, p. 995-1004
University of Antwerp
In previous papers we derived sufficient conditions for linear stability of spherically symmetric and spherical, axisymmetric, gravitating configurations in ideal magnetohydrodynamics by using the general theory of Arnold and Vladimirov et al. The same general theory is now used to deduce sufficient conditions for linear stability of two-dimensional gravitating configurations with perpendicular magnetic field. Again a helpful analogy between two-dimensional magnetohydrodynamic flows subjected to a self-gravitating force field (or a pseudo-gravitating one) and flows of stratified fluids in the Vladimirov-Boussinesq approximation is obtained. A "modified vorticity field" is considered which turns out to be an additional frozen-in field like the vector potential of the magnetic field. This allows to construct a general Casimir functional. From the latter a linear stability criterion is obtained.