Hydromagnetic Rayleigh--Taylor instability of a rotating stratified fluid

The Raleigh--Taylor instability of an infinitely conducting, rotating, stratified fluid in the presence of a horizontal magnetic field is studied. The fluid density and the magnetic field strength are arbitrary functions of the vertical coordinate. An estimate of the upper bound for the growth rate of the instability of any unstable mode of disturbances of a given wavelength, which cannot occur unless the fluid density increases with height at some points, is obtained. This estimate is found to give a satisfactory result in a Rayleigh--Taylor instability model for which the dispersion relation is known exactly. A sufficient condition for stability of a disturbance is also obtained