Beyond ray tracing for internal waves. II. Finite-amplitude effects

Abstract

We examine the transmission of small and moderately large internal gravity wavepackets through uniformly and nonuniformly stratified fluids using fully nonlinear numerical simulations. The simulations of finite-amplitude waves in a uniformly stratified fluid show that the weakly nonlinear theory developed for horizontally periodic wavepackets extends well to the dynamics of wavepackets with horizontal extent comparable to the horizontal wavelength. In simulations of small-amplitude wavepackets in a nonuniformly stratified fluid the transmission coefficient is found to be comparable to that computed analytically for horizontally periodic waves that radiate continuously (nontransiently) on a reflection level. Simulations of finite-amplitude waves in a nonuniformly stratified fluid show little dependence of transmission coefficient on the wavepacket extent. However, for a wide range of incident wave frequencies the simulations exhibit a monotonic increase in the transmission coefficient as a function of the incident wave amplitude.