Calculations of Caustic Lines in an Ocean of Constant Velocity Gradient Layers

Abstract

It is generally recognized that caustics exist in convergence zones near the surface of the ocean. The shapes of these caustic lines along their entire extent from the surface to the bottom of the ocean has been recently studied. Each caustic line consists of two branches connected at a cusp where the caustic first appears caused by a folding wave front. A systematic study of the formation of caustics in media of constant velocity gradient layers has been made. The study starts with the infinite medium with one isovelocity layer above one constant gradient layer and progresses to a many layered ocean closely approximating a real velocity profile and limited by a surface. Calculations of ray paths and wave fronts were made with the IBM 709 computer in order to determine the caustic lines. Plots of range versus initial angle were used to explain points of interest on the caustics. The effects of surface shadow on the caustic lines were shown, and wave fronts in this region were explained. It was found that a two-layer ocean demonstrates the essential features of the caustic lines.