Stability Of Magnetohydrodynamic Shear Flows

A study is made of the stability of a stratified shear flow in a perfectly conducting fluid in the presence of an external magnetic field aligned with the flow. A sufficient condition for stability of the flow is derived. A semi-circle theorem for the present hydromagnetic case is proved. The magnetic field is found to have a stabilizing effect on the flow. In order to incorporate the effects of density stratification, the semi-circle theorem is refined further to give a semi-ellipse theorem