A unified instability criterion for heterogeneous shear flows

Conditions are defined for the formulation of unified criterion of instability for heterogeneous shear flows with a density which monotonically decreases with altitude. A simultaneous reduction of Howard's semi-circle theorem is demonstrated, as is the existence of a limit on the range of the complex wave velocity of an arbitrary unstable mode. The criterion is shown to extend the class of velocity and density distributions previously defined by other researchers.