Internal waves in a horizontally inhomogeneous flow

Abstract

The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal surfaces. It is shown that internal-wave blocking and short-wave transformation may occur in longitudinally inhomogeneous flows. For parallel flows internal-wave trapping is possible in the vicinity of the limiting layer where the wave frequency in the locally comoving frame of reference coincides with the Brunt-Väisälä frequency. Internal-wave trapping also takes place in jet-type flows in the vicinity of the flow-velocity maximum. WKB solutions of the equation describing internal-wave propagation in a parallel horizontally inhomogeneous flow in the linear approximation are obtained. Singular points of this equation and the related effect of internal-wave amplification (overreflection) under the action of the flow are investigated. The spectrum and the growth rate of internal-wave localized modes in a jet-type flow are obtained.