Some mathematical problems of numerical ocean acoustics
(From author's abstract.) The wave equation \(\phi_{tt}=c^ 2[\phi_{xx}+\phi_{yy}+\phi_{zz}]\) and the Helmholtz equation \(\nabla^ 2\phi +k^ 2\phi =0\) provide classic analytical models for predicting the propagation of sonar wave packets and SOFAR wave packets in a homogeneous ocean. In this paper an analysis is made of problems encountered in integrating these partial DEs numerically, especially in the presence of boundaries. Then comments are made on correcting such computations for known refraction. These comments center around the concept of a 'simple' sound wave, whose particle orbits satisfy \(\phi\) (\b{x};t)\(=A(\underline x)\cos <\omega [t-\tau (\underline x)]>\); the case \(\tau\) (\b{x})\(=const\). defines 'standing waves'. Finally, attention is called to the problem of modelling some physical phenomena ignored in most mathematical models of ocean acoustics.
scientific article; zbMATH DE number 3988983