An instability criterion for a finite amplitude localized disturbance in a shear flow of electrically conducting fluids

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for the case of low magnetic Reynolds number is obtained by integrating analytically the vorticity equation. Analysis of the resulted equation reveals a new instability criterion.