Mode formulas for shallow water waveguides using a modified asymptotic approximation

Abstract

Sound speed profiles in shallow water waveguides are small deviations from isospeed and often decrease monotonically with depth. Approximation formulas for the propagating modes are found using a modified form of the classical WKBJ method. The ocean bottom is taken as homogeneous. The approach is accurate for modes with phase speeds greater than, and even slightly less than, the maximum water sound speed. The validity and accuracy of the approximations over frequency and mode number are illustrated using benchmark numerical calculations. Comparisons with approximations from other methods, including previous WKBJ approaches, are described. The formulas here are typically more compact and convenient. The results demonstrate how changes in parameters, such as frequency, bottom sound speed, and water sound speed profile quantitatively affect the mode functions. Applications for representative waveguide profiles are provided. [Work supported by the Office of Naval Research.]

Shallow Water Propagation

“…To determine dependence on environmental parameters and frequency conveniently, perturbation approximations are constructed [19] for mode shapes and wave numbers for a class of downward refracting sound speed profiles. These results are extended by developing two other asymptotic modal approximations [20], which are valid for complementary sets of parameter values and consequently are useful together for applications. Specifically, we examine modal attenuation coefficients [21], on which the influence of sound speed gradients at different locations in the water column is found in terms of environmental parameters.…”

Efficient Determination of Three-Dimensional Acoustic Fluctuations in Shallow-Water Waveguides

“…For cases such as a linear downward refracting profile, the modal amplitude at the water sediment interface approaches a constant for high frequencies. In contrast, for environments that are upward refracting in the lower water channel, the interfacial modal amplitude decreases exponentially with frequency [4]. These variations are useful in explaining and predicting the behavior of the modal attenuation coefficients, for example.…”

Shallow Water Propagation

“…Expressions for modal attenuation coefficients are examined [16] using new modal approximations in order to show the influence of sound speed gradients at different locations in the water column. These modal approximations are convenient for applications because they are developed from two asymptotic approaches [17] that are valid for complementary regimes of parameter values. Connections between the frequency dependence of modal attenuation coefficients and the attenuation of averaged reduced transmission loss are quantified [18] by showing the primary dependence on features of the water sound speed profile.…”