Efficient Determination of Three-Dimensional Acoustic Fluctuations in Shallow-Water Waveguides
2010
Siegmann, William L. | Kaczkowski, Stephen V.
Many shallow water waveguides have sound speed profiles that are small deviations from isospeed, so that perturbation methods can be applied to obtain approximate formulas which are valid for modes and parameter values of interest. We develop two-term asymptotic modal formulas that are concise and more convenient than numerical or series representations. The formulas are designed to be useful for determining parameter dependences of relevant acoustic quantities. The main restrictions are to propagating modes, to assuming range dependence is negligible or adiabatic, and to fast isospeed bottoms with sound speed Cb exceeding the maximum water sound speed Ch. The perturbation parameter is the relative difference of Ch and a reference water speed. The approach uses the modified, or generalized, Green's function. Solution formulas are compared with those from variation of parameters and resolvent kernel methods [1]. The primary ocean waveguide environments considered have thermocline sound speed profiles with isospeed layers above and below a middle layer of decreasing sound speed. Comparisons of the formulas are made with numerical calculations over a range of frequencies and mode numbers. The results [2] show that the approximations are accurate for modes with phase speed vn higher than Ch, and that accuracy improves as mode number increases and as depth in wavelength decreases.
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