Parameter sensitivity of acoustic propagation in models of curved fronts over uniform slopes

Abstract

A modification of the sloping bottom curved front model including continuous sound speed variation is examined for the importance of front width. Analysis of parameter sensitivity in the idealized front is used as a baseline for comparisons. The proposed model for a continuous front includes a range dependent sound speed representation chosen for mathematical convenience. Using the same physical derivation of mode number conservation and confirmation through asymptotic approximation, the continuous front model yields convenient equations for parameter dependence of along-front wavenumber. These equations agree with the idealized front results for the real part of the horizontal wavenumber as the front width diminishes, and captures the significantly altered behavior of modal attenuation coefficients. A comparison of partial Transmission Loss (TL) fields for the idealized and continuous fronts further illustrates the behavioral differences between a sharp front and fronts of varying width. These differences include leaky modes that decay faster along shore in the continuous front than analogous modes in the idealized front, as well as the introduction of near-resonant modes which have a significant effect on the near-field and do not exist in the idealized front formulation.

In a coastal sloping bottom ocean environment, sound speed fronts can form and create a ducting effect of along-front acoustic propagation. The structure and behavior of horizontal acoustic modes for a three-dimensional idealized model of a shelf-slope front are examined analytically. The Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method is used to obtain convenient simple expressions and to provide physical insight into the structure and behavior of horizontal modes as trapped, leaky, or transition types. The 3D shelf-slope front ocean feature model is parameterized by environmental and acoustic quantities including front location, bottom slope angle, source frequency, and sound speed. Changes in these quantities cause changes in the modal phase speeds, which in turn are determined from the real and imaginary parts of the modal horizontal wavenumbers. A derivation of mode number conservation for an idealized sharp front leads to a convenient and accurate physically meaningful formula for parameter dependence of the real part of horizontal wavenumbers. This formula is confirmed using asymptotic approximations of the dispersion relation, and the confirmation technique also leads to accurate approximations of along-shore modal attenuation coefficients, which are the imaginary components of horizontal wavenumber. The attenuation coefficients are sensitive to transitions between different radial mode types. Local approximations of these equations characterize the sensitivity to small parameter variations; for example, wavenumbers are most sensitive to changes in frequency and inshore sound speed, and least sensitive to changes in offshore sound speed.