Internal gravity waves: critical layer absorption in a rotating fluid

Abstract

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 2ΩV, 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 Wg is the vertical group velocity, 2ΩH is the horizontal component of the Coriolis parameter, l and m are the easterly and northerly wavenumber components, and Uz and Vz 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(Uz + 2ΩH) − lVz]/(lUz + mVz)|}. The phenomenon is also analysed using a WKBJ approximation.