A modal Wentzel-Kramers-Brillouin approach to calculating the waveguide invariant for non-ideal waveguides

作者：Cockrell Kevin L^*; Schmidt Henrik

来源：Journal of the Acoustical Society of America, 2011, 130(1): 72-83.

DOI：10.1121/1.3592236

The frequency dependence of a waveguide's Green's function can be summarized by a single parameter known as the waveguide invariant, beta. Although it has been shown analytically that beta approximate to 1 for ideal waveguides, numerical and experimental results have shown that beta approximate to 1 for many realistic shallow water waveguides as well. There is not much prior work explaining why the non-uniformities present in realistic sound speed profiles sometimes have such a small effect on the value of beta. This paper presents a method for calculating beta using a modal Wentzel-Kramers-Brillouin (WKB) description of the acoustic field, which reveals a straightforward relationship between the sound speed profile and beta. That relationship is used to illustrate why non-uniformities in the sound speed profile sometimes have such a small effect on beta and under what circumstances the non-uniformities will have a large effect on beta. The method uses implicit differentiation and thus does not explicitly solve for the horizontal wavenumbers of the modes, making it applicable to waveguides with arbitrary sound speed profiles and fluid bottom halfspaces. Several examples are given, including an analytic estimate of beta in a Pekeris waveguide.

• 出版日期2011-7