Mean flow generated by a reflecting internal wave packet

The mean flow created by reflecting internal waves at a horizontal interface between layers of constant buoyancy frequency (a density gradient interface) is treated with weakly nonlinear theory. The interface is a simple model of the atmospheric tropopause. Previous work has assumed horizontal periodicity, but here we relax that assumption and treat waves that are confined to a long wave packet in the horizontal. The mean flow generated by a reflecting train of internal waves has two parts: 1) a part driven by the modulation, which would be obtained if incident and reflecting waves acted individually, and 2) a part caused by the direct interference of incident and reflecting waves. For the two-dimensional theory, scaling shows that the interference mean flow is several orders of magnitude larger than the modulation mean flow, which is neglected. The leading order mean flow equations are linear and are solved with Fourier transforms. Detailed results are obtained for a Gaussian wave packet. The mean flow is weak for steep and shallow carrier waves, and strongest when the carrier waves ascend at approximately 57 degrees. The mean flow has an external (outside of the packet) component that consists of a spectrum of inertia waves traveling both upstream and downstream. For shallow carrier waves the upstream component is stronger.