Magnetohydrodynamic Wave-Energy Flux in a Stratified Compressible Atmosphere With Shear

The full wave equation is derived for motion in a compressible, perfectly conducting stratified atmosphere, with a shear flow along a horizontal magnetic field. Expressions are derived for the vertical distribution of mechanical energy flux ℱ(z) as a function of altitude, and a number of stability results are established on the basis of a normal mode energy-flux function ℱ˜(z;k,ω) . These include a semicircle theorem; and a sufficient condition for stability against shear (not necessarily for stably-stratified media) in a magnetoatmospheric régime.