Internal wave reflection in uniform shear

If nonhydrostatic internal waves are of sufficiently large amplitude, they undergo significant dispersion due to interactions between the waves and wave-induced mean flow. The effect of these interactions is investigated for internal waves propagating upward in a uniformly stratified Boussinesq how with uniform shear. The sign of the shear is established so that the wave intrinsic frequency increases as the wave packet propagates upward; hence linear theory predicts that the waves should reflect at some level. Fully nonlinear numerical simulations of two-dimensional wave packets are performed to study the wave-packet evolution as a function of the initial amplitude and spatial extent of the wave packet. It is shown that if the waves are horizontally periodic, and of sufficiently large amplitude, momentum is permanently deposited to the mean flow at altitudes near, but below, the reflecting level predicted by Linear theory. If the waves are horizontally compact, the waves propagate upward well above the reflection level.