KELVIN-HELMHOLTZ INSTABILITY UNDER HORIZONTAL ROTATION AND MAGNETIC-FIELDS

The author's previous work on the Rayleigh-Taylor instability is exten ded to the Kelvin-Helmholtz instability, and the maximum growth rate o f a perturbation and an estimate of its upper bound is obtained for an infinite fluid layer under horizontal rotation where the density, hor izontal velocity (shear) and magnetic field are continuously stratifie d in the direction of gravity. Conclusions are drawn about the possibi lity of stability for some directions of propagation of the perturbati on, even in the case of unstably stratified density. It is also shown that the new terms that appear owing to the interaction of the horizon tal shear flow, horizontal rotation and stratified magnetic field incr ease the range of values that contribute to the estimate of the maximu m growth rate compared with previous work. Furthermore, a generalizati on of the sufficient condition for stability under horizontal rotation alone obtained by Johnson is calculated in the presence of density st ratification. A new method is also given to obtain a sufficient condit ion for stability when a magnetic field is present in addition to rota tion and density stratification.