On the stability of a thermally stratified conducting fluid under the action of aligned magnetic field

The stability of a thermally stable stratified viscous electrically conducting shear flow is investigated in the presence of an impressed uniform aligned magnetic field. Only two-dimensional disturbances are studied in this paper because Squire's theorem does not apply in general, owing to the presence of the aligned magnetic field. The analysis is partly analytical and partly numerical. The asymptotic solutions for non-viscous fluid are first obtained analytically and they are then improved by introducing viscous and thermal diffusion terms (but only for σ =1) to get a uniformly valid solution. The neutral stability curves are numerically computed for a range of values of Richardson and Stuart numbers, which show that the flow is completely stabilized when a Stuart number exceeds a certain value for a given R i > 0. It is shown that the combined effects of magnetic field and stratification is to make the system stable to two-dimensional disturbances at lower Stuart number than the one given by Stuart (1954) in the absence of thermal stratification