A THEORETICAL ANALYSIS OF ACOUSTIC WAVE MODES IN LAYERED LIQUIDS
Abstract
The fundamental acoustic pressure and particle velocity field and wave equations were derived for a vertically stratified, slightly viscous medium in which the small viscous effect was carried through only as a first-order correction term. The wave fields resulting from a single frequency point source in 3 particular media were derived and expressed as a sum of modes. The first 2 media were 1- and 2-layered homogeneous liquids bounded by perfectly reflecting planes, while the third was the Pekeris configuration (Geol. Soc. Amer., Mem. 27, 1948). The modes in the 3 systems were compared with respect to orthogonality, completeness, finiteness, modal identity and discreteness, physical representations, and cut-off. A study was also made of some characteristics of generally valid acoustic modes. Particular emphasis was placed upon the derivation of the power and energy orthogonality conditions and the physical interpretations of the propagation factors from energy considerations. These problems are restricted to vertically stratified systems in the cylindrical coordinate system, but the methods are adaptable to general wave problems in other coordinate systems provided the stratification does not lie along the preferred direction of wave propagation. The application of the results to the numerical calculation of acoustic fields in shallow-water problems is severely limited by the idealized representation of the medium as a system of homogeneous liquid layers. However, a relatively simple explanation is provided by these idealized models of the physical processes occurring in shallow-water sound-transmission media.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1953
- Accession Number
- AD0015837
Entities
People
- Jack L. Stone
Organizations
- Princeton University