Internal gravity waves: critical layer absorption in a rotating fluid

The propagation of internal gravity waves in a shear flow in a rotating fluid is examined for the case when the rotation vector is inclined to the vertical. It is shown that internal gravity waves approaching a critical level, where ω*, the Doppler-shifted frequency, equals 2Ω_V, the vertical component of the Coriolis parameter, will be either transmitted or absorbed according as \[ W_g\omega^{*}2\Omega_V\{m(U_z + 2\Omega_H)-lV_z\}\lessgtr 0; \] here W_g is the vertical group velocity, 2Ω_H is the horizontal component of the Coriolis parameter, l and m are the easterly and northerly wavenumber components, and U_z and V_z are the shear rates of the easterly and northerly components of the mean flow. Between critical levels, wave action flux is conserved. However, for a wave absorbed at a critical level, the wave action flux is attenuated by a factor exp { − 2π|m(U_z + 2Ω_H) − lV_z]/(lU_z + mV_z)|}. The phenomenon is also analysed using a WKBJ approximation.