An accurate, efficient rough surface parabolic equation program

Abstract

The parabolic equation program Fepe has been extended to handle a rough air–water interface treated as a series of stair steps. Because much finer vertical spacing may be needed to resolve the interface than to propagate an acoustic wave accurately in the rest of the domain, an option to use one vertical spacing near the surface and a coarser one in the rest of the ocean has been implemented. The necessary Galerkin approximations of derivatives on an unequally spaced grid have been worked out using the symbolic manipulation program Mathematica. A test case with a realistic surface is provided to demonstrate the accuracy of the new program Fepe–rsfc. The code is efficient enough to allow thousands of runs for realistic sized problems, for example to simulate the effect of a moving surface. [Work supported by the office of the Chief of Naval Operations.]