Abstract

Some general results on the stability of a compressible parallel shear flow permeated by an aligned magnetic field are derived. It is shown that the complex wave speed of an unstable wave lies in a semi-circle in the upper half plane with the range of the shear flow as diameter. Further both compressibility and magnetic field are found to be stabilizing. It is also shown that in a flow near a wall, two acoustic waves carry energy away from the wall. A semi-circle theorem for a non-planar compressible shear flow is also deduced.

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