On the character of magnetic field in the hydromagnetic generalized Benard problem

The stability of a continuously stratified layer of viscous incompressible fluid of finite electrical conductivity statically confined between two horizontal and perfectly conducting boundaries of different but uniform temperature in the presence of a uniform vertical magnetic field acting opposite to the direction of gravity has been investigated. The initial stratification which might be produced for example by a dissolved solute of negligible diffusitivity is assumed to be of the exponential type namely rho=rhosub(0)esup(-deltaz) where delta is a constant which can be positive or negative and thus makes the initial stratification a monotone decreasing or increasing function of z respectively, rhosub(0) is a positive constant and z the vertical coordinate while the temperature of the lower boundary is taken to be greater than that of the upper one. It is shown that marginal state, if exists, is definitely oscillatory. Further, for negative values of delta the system is unstable while for delta > 0 the Rayleigh number and the frequency of oscillation are calculated at the marginal state and the stabilizing character of the magnetic field is established in situations where the magnetic Prandtl number is less than the thermal Prandtl number, a condition which is met by a large margin under most terrestrial conditions. (auth.)