Statistics of the forward field propagated through three-dimensional random internal waves in an ocean waveguide.

Abstract

Internal waves randomize the forward propagated acoustic field in both continental shelf and deep water environments. This has implications in underwater communications and remote sensing using wide area sonar systems. Here, we derive compact analytic expressions for the mean, variance, mutual intensity, spatial covariance, and temporal coherence of the acoustic field propagated through three‐dimensional (3‐D) random internal waves. These take into account multiple forward scattering effects and are derived in terms of the statistics of the internal waves. For typical continental shelf environments, we show that when internal wave height exceeds the acoustic wavelength, the acoustic field becomes so randomized that the expected total intensity is dominated by the field variance beyond moderate ranges. This leads to an effectively saturated field that decays monotonically and no longer exhibits the periodic range‐dependent modal interference structure present in nonrandom waveguides. 3‐D scattering effects become important when the Fresnel width exceeds the cross‐range coherence length of the internal wave field. Our derivation makes it possible to predict the coherence time scale of field fluctuations in ocean‐acoustic measurements from knowledge of the oceanography. It is used to explain the time scale of acoustic field fluctuations observed at megameter ranges in various deep ocean‐acoustic transmission experiments.