Geographically localised shelf waves on curved coasts

This paper presents a combined analytical and numerical extension to recent theoretical work on trapped continental shelf waves over smoothly curved coastlines. The geometry considered consists of an annular region joining two semi-infinite straight sections and, even though the isobaths remain evenly spaced, trapped modes appear in the annular region due entirely to the longitudinal curvature of the shelf there. Expanding in alongshore modes and requiring that the error is orthogonal to the transverse modes gives a linear algebraic system of equations for the frequency of trapping. Solutions for barotropic, non-divergent shelf waves show that trapped modes always exist if the coastline curves to form a headland.