Large amplitude internal gravity wavepacket propagation

Simple heuristics based on ray theory predict that small amplitude internal waves reflect off constant density layers in an otherwise uniformly stratified background fluid. These heuristics are based on the assumption that the vertical scale of variations in the background are large compared to the vertical wavelength of waves. However, if the unstratified layer is shallow compared to the vertical wavelength, internal waves can `tunnel' across the layer and propagate beyond it. Using the ratio of transmitted to incident pseusdoenergy flux an analytic prediction was found for the transmission of incident small amplitude, plane waves through an unstratified layer. Here we extend this work to examine the transmission of vertically and horizontally localized internal gravity wavepackets. In this case, we use the ratio of the time averaged transmitted to incident pseudoenergy flux to measure the transmission of the wavepackets. Numerical simulations of small-amplitude wavepackets show the transmission is within one percent of the linear theory prediction for the transmission of horizontally periodic waves. For moderately large amplitude wavepackets, with maximum vertical displacement between four and eight percent of horizontal wavelength, the transmission of pseudoenergy increases by up to twenty percent. Applications to the atmosphere will be discussed.