Linear stability criterion for steady screw magnetohydrodynamic flows of ideal fluid

Abstract

A linear stability problem for a subclass of steady screw flows of a uniform-density inviscid incompressible ideally conducting fluid in the magnetic field is investigated. The necessary and sufficient condition of theoretical (in semi-infinite time intervals) stability as well as the sufficient conditions for the practical (in finite time intervals) instability of the given flows to small screw disturbances are obtained by the direct Lyapunov method. In the case when the theoretical stability criterion is violated, and the sufficient conditions of practical instability are valid, on the contrary, an a priori exponential estimate from below has been derived for the growth of small disturbances under consideration, and the increment of the exponent contained therein is an arbitrary positive constant.