Propagation and reflection of internal waves

Fully nonlinear numerical simulations are performed to examine the behavior of large-amplitude internal gravity waves incident upon a level where the Doppler-shifted frequency of the waves is comparable to the background buoyancy frequency. Although linear theory predicts that the waves should reflect if the Doppler-shifted frequency is greater than the buoyancy frequency, it is found that nonlinear effects may greatly enhance the transmission of a wave packet across a reflecting level. If the Doppler-shifted frequency is moderately less than the buoyancy frequency, then nonlinear effects may greatly enhance the reflection of waves. A range of simulations is performed to characterize the reflection coefficient as a function of the amplitude and spatial extent of the wave packet. In comparison with horizontally periodic wave packets, it is found that the nonlinearly enhanced transmission of wave packets is more significant if they are horizontally compact. This occurs because the wave-induced mean flow effectively increases and decreases the horizontal phase speed of the waves on the incident and trailing flank of the wave packets, respectively, and this significantly broadens the frequency spectrum of the waves. © 1999 American Institute of Physics. @S1070-6631~99!01205-2#