Exact edge wave solutions for some generalised exponential shelf topographies

Source abstract

Abstract Exact wave-height solutions are presented for trapped waves over two new three-parameter depth topographies. Dispersive properties are calculated for both a semi-infinite and a truncated convex exponential profile, as well as for a semi-infinite concave profile. The analysis in all three cases is general in that both horizontal divergence and rotational effects are included. These solutions may be used for either high-frequency edge wave or low-frequency shelf wave studies by taking appropriate limits ( f → 0 for edge wave and ε = f 2 L 2 / gH ≪ 1 for shelf waves).