Hydromagnetic stability of compressible fluid

Abstract

The hydromagnetic stability of an adiabatic compressible perfectly conducting non-viscous fluid is investigated and it is shown that a necessary condition for instability is J_H < 1/4P⁺ + g²/ C²(W')² where J _H is the Richardson number, P ₊ the magnetic parameter, C the acoustic velocity, W' the basic velocity shear and g the gravity. This condition for instability is useful in studying the propagation of internal Alfven-acoustic- gravity waves across a critical level.