Tide-topography interaction

Abstract

An analytical method is reviewed that enables the construction of two-dimensional topographies for which tidal conversion is absent. The method employs the analogue of conformal mapping to solve the tide-generation problem exactly. In this problem, a spatial hyperbolic equation governs the streamfunction eld that reaches constant values at bottom and surface, and that is subject to a radiation condition far away from any topographic features present. This problem in principle governs both the trapped, nonhydrostatic (depth-dependent) barotropic, as well as propagating, internal wave response. But, employing the mapping, only the former, trapped eld is obtained. For a particular class of localized ridges, we here verify this by constructing the same nonhydrostatic barotropic eld in an entirely independent manner.