Analytical Solution for Benchmark Problem 1: The 'ideal' Wedge

摘要

Over the past decade or so, several computer codes have been developed forcalculating the sound field in complex underwater environments. These algorithms are based on numerical solutions of the wave equation (or related equations) and are very complicated, generally requiring long run times to arrive at a final estimate of the field. Most, if not all, of these codes are based on some more or less subtle form of approximation. After many hours of CPU time, when the estimate for the field is finally produced, the question inevitably arises: How accurate is the result. There is no simple answer to this enquiry because, for most range-dependent ocean channels, no reference solution exists. This problem has been recognized by the ocean acoustics community for some time, and was addressed recently in two benchmark sessions at consecutive meetings of the Acoustical Society of America. At the first of these meetings, three range-dependent problems were specified, bench-marks 1, 2, and 3, to be used as test cases for comparing the various propagation models, one with another. The purpose of this reprint is to present an analytical solution for benchmark problem 1, which is the two-dimensional, ideal wedge problem: The acoustic field is required in a wedge, with pressure-release boundaries, which contains a line source parallel to the apex. This is one of the few range-dependent problems with an exact analytical solution. The form of this solution is outlined below, and transmission loss results evaluated from it are given graphically. Comments are included about the evaluation procedure and the care that was exercised to eliminate errors. (kr)