Internal gravity wave radiation into weakly stratified fluid

Abstract

It is shown by way of nonlinear numerical simulations of flow restricted to two dimensions that a compact wavepacket of large-amplitude internal gravity waves incident upon a weakly stratified region in which the buoyancy frequency is less than the frequency of the wavepacket may partially transmit energy into this region through the generation of a wavepacket of lower frequency. In part, the transmission of waves occurs due to the transient nature of the forcing by the incident wavepacket, but if the amplitude of the wavepacket is moderately large, weakly nonlinear effects may act to significantly increase the proportion of the wavepacket that is transmitted. For a range of simulations initialized with wavepackets of different amplitude and vertical extent, the characteristics of the reflected and transmitted waves are analyzed and reflection coefficients are calculated. An explanation for how the nonlinear transmission mechanism operates is given by demonstrating that the wave induced mean-flow, which is shown to be approximately equal to the horizontal wave pseudomomentum expressed in Eulerian variables, acts to adjust the frequency of the incident waves.