Low-frequency scattering of Kelvin waves by continuous topography

Abstract

This paper continues the analysis of Johnson (1990, hereinafter referred to as I) of the scattering of Kelvin waves by collections of ridges and valleys. General results, flow patterns and explicit solutions follow by restricting attention to waves whose period is long compared to the inertial period but without the additional further simplification introduced in I of approximating general features by stepped topography. A simple direct method is presented giving explicit formulae for the amplitude of the transmitted Kelvin wave and the scattered topographic long waves. A simple but accurate approximation to the solution is also given. The accuracy and usefulness of the apparently crude method of I are confirmed and a superior method presented for choosing the positions of steps in the approximation of general topography. Inviscid flows, the effects of weak dissipation and weak stratification, the form and relevance of the short-wave field over downslopes, the partition of mass and energy flux between the long-wave and short-wave fields and the size and form of higher-order effects are also discussed.