Some Mathematical and Computational Contributions to Underwater Sound Propagation

Abstract

This study of underwater acoustic propagation seeks, first, to determine just what can be known concerning the medium (velocity as a function of position and time, conditions of bottom and surface, etc.), so that the mathematical inferences therefrom can be realistic; second, to apply to this purpose the most powerful modern mathematical tools; third, to implement the results by efficient methods of numerical computation. Starting with the standard wave equation and energy-flux vector, specializations are made for traveling waves of high frequency, in which the energy flux is along the bi-characteristics (rays). To the latter are applied Hamiltonian methods: perturbation theory, integral, invariants and statistical information theory, etc. The wave is also treated directly by modern mathematical methods. The numerical methodology takes advantage of these analytic results, and is further simplified by avoiding levels of detail inconsistent with the levels of knowledge. Relatively simple and powerful computer programs are developed when sound speed depends on depth only; they are extended by perturbation methods to a more general case, including small but not negligible horizontal gradients. The statistical effects of fluctuations of actual from average profiles are examined. [Work was supported by the Naval Ordnance System Command.]