Scattering of Long Divergent Shelf Waves by a Thin Barrier Parallel to the Coast

Abstract

The barotropic shallow-water equations and exponential topography are used to investigate the low-frequency scattering of an incident shelf wave by a thin barrier located parallel to the coast by means of eigenfunction matching techniques, following Hsieh and Buchwald. In this model, however, the nondivergent (rigid-lid) approximation is relaxed, and hence, we are able to compute the energy in the Kelvin modes. In order for the problem to be well posed, we consider a barrier of finite 1ength in an infinite channel with a rigid wall at the shelf edge. The wall supports a reflected Kelvin wave traveling in the direction opposite to the incident shelf wave. The problem is then formulated in term of the unknown amplitude of this reflected Kelvin wave and solved using the radiation condition that no energy is incident on the barrier from the downstream side of the channel. Energy flux computations show that a large fraction of the energy in an incident mode 1 is transferred to the Kelvin mode in the region between the barrier and the coast. Although we found that the model is not well posed when the barrier length tends to infinity, the results are consistent with recent observations that incoming shelf-wave energy is responsible for much of the low-frequency Kelvin wave forcing in Bass Strait, southeast of Australia.