A ray method for near-shore plumes in a shallow-water flow

Far from a shoreline, the spreading of a contaminant plume in a shallow-water flow can be predicted easily and accurately by a ray-tracing method. Unfortunately, the concentration predictions become singular at a beach, where the ray paths have a caustic. In this paper a uniform approximation is derived which remains valid at a beach. It is shown how the singular ray solutions corresponding to rays incident to and transmitted from the beach can be combined to construct the uniform approximation.