Internal waves in a 2D subcritical channel

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.

17 pages, 3 figures. The first version of this manuscript contained an account of the limiting absorption principle, together with consequences for the long-time asymptotics in the time-dependent problem with periodic forcing. We have, however, discovered an error in this work, and anticipate returning to the question of the limiting absorption principle in a future work