Steady and unsteady nonlinear internal waves incident on an interface

Steady nonlinear internal waves are commonly described by the Dubreil-JacotinLong equation. This equation contains unknown functions of the stream function, representing the density and vorticity fields. Often these are determined by upstream conditions where the flow is assumed to be known. But for the case when the waves are periodic in the horizontal direction, these functions need to be determined instead by consideration of the source of the waves, and in particular by the wave-induced mean flow. Here we show that this situation is particularly important for waves incident and reflected from an interface, representing a sharp change in the background density stratification, such as that at the tropopause. The combination of the incident and reflected wave-induced mean flows generates a sharp shear near the interface.