Valve like critical levels for internal gravity waves in compressible shear flows

The propagation of internal gravity waves in, isothermal compressible shear (both vertical and horizontal) flows are investigated. In slowly-varying shear flows the local dispersion relation is used to study the wave-normal surfaces and the possible types of ray trajectory. Of the seven, singular levels for the wave equation only two offer resistance to wave propagation and these two exhibit valve like behaviour. It is observed that though the effect of compressibility does not increase the number of critical levels it modifies the position of the critical levels and the attenuation of waves at the critical levels. In a slowly varying medium it is observed that only these two critical levels are present and strictly behave like valves, In a full wave treatment it is demonstrated that compressibility decreases the amount of attenuation of each wave at its critical level. MSC (1991): 76F10, 76N10.