Scintillating shallow-water waveguides

An analysis of acoustic wave propagation in a random shallow-water waveguide with an energy absorbing sub-bottom is presented, in which deviations of the index of refraction are a stochastic process. The specific model studied is motivated by the oceanic waveguide in shallow waters, in which the sub-bottom sediment leads to energy loss from the acoustic field, and the stochastic process results from internal (i.e., density) waves. In terms of the normal modes of the waveguide, the randomness leads to mode coupling while the energy loss results from different attenuation rates for the various modes (i.e., mode stripping). The distinction in shallow water is that there exists a competition between the mode-coupling terms, which redistribute the modal energies, and mode stripping, which results in an irreversible loss of energy. Theoretically, averaged equations are formulated for both the modal intensities and fluctuations (the second and fourth moments of acoustic pressure, respectively), similar to previous formulations which, however, did not include the effects of sub-bottom absorption of acoustic energy. The theory developed here predicts that there is a mismatch between decay rates between the second and fourth moments, implying that the scintillation index (which is a measure of the strength of the random scattering) grows exponentially in range. Thus the usual concept of equilibrium or saturated statistics must be modified. This theoretical prediction is generally valid and depends only on assuming the forward scattering approximation, the Markov approximation (i.e., the short-range nature of the correlations between sound-speed fluctuations) and neglecting the cross-modal coherences. In order to assess the importance of these assumptions Monte Carlo simulations of stochastic coupled-mode equations are presented. For these simulations, models of internal-wave processes, deterministic shallow-water acoustic environments, and sub-bottom attenuation that simplify the numerical computation were chosen. While these models are unrealistic they illustrate the theoretically predicted behavior.