Internal waves in a 2D subcritical channel

TL;DR

This paper studies how linear internal waves scatter in a 2D channel with subcritical bottom topography, constructing a scattering matrix and proving unique solvability of the scattering problem.

Contribution

It introduces a novel construction of the scattering matrix for internal waves in a 2D channel with subcritical topography, linking it to ray-tracing dynamics.

Findings

Scattering matrix differs from the bounce map by a smoothing operator.

Unique solvability of the scattering problem under outgoing radiation conditions.

Provides a mathematical framework for internal wave scattering in channels.

Abstract

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to outgoing data; this operator turns out to differ by a smoothing operator from the pullback by the ``bounce map'' for boundary data obtained by ray-tracing. As a consequence we obtain unique solvability of the inhomogeneous stationary scattering problem subject to an appropriate outgoing radiation condition.