Some mathematical problems of numerical ocean acoustics
type: Item
instance of: scholarly article
title: Some mathematical problems of numerical ocean acoustics
zbMATH Open document ID: 0611.76088
DOI: 10.1016/0898-1221(85)90161-0
publication date: 1985-01-01T00:00:00Z
review text: (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.
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 3988983
zbMATH Keywords: wave equation
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: propagation of sonar wave packets
zbMATH Keywords: SOFAR wave packets
zbMATH Keywords: homogeneous ocean
zbMATH Keywords: refraction
zbMATH Keywords: sound wave
zbMATH Keywords: standing waves
zbMATH Keywords: ocean acoustics
author: Garrett. Birkhoff
reviewed by: John E. Ffowcs Williams
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90161-0
OpenAlex ID: W2010082673
cites work: Q5799828
cites work: The Inverse Scattering Problem for Time-Harmonic Acoustic Waves
cites work: Q5812445
cites work: Progress and Prospects in the Theory of Linear Wave Propagation
cites work: Wave propagation and underwater acoustics
cites work: Q5736106
cites work: Q3002668
cites work: L'intégrale de Riemann-Liouville et le problème de Cauchy
cites work: Q4151274
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3988983