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Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.

A numerical study of beamforming on a horizontal array is performed in a shallow water waveguide where a summer thermocline is perturbed by a time evolving realization of an internal wave field. The components of the internal wave field consist of a horizontally (azimuthally) isotropic, spatially homogeneous contribution, and a horizontally anisotropic, spatially inhomogeneous component. These terms represent a diffuse ("background") internal wave field and a localized solitary wave packet, respectively. Conventional beamforming is performed as a function of time while the internal wave field evolves throughout a computational volume containing the source-receiver paths. Source-receiver orientation with respect to the azimuthally anisotropic component has a significant effect on the beamformed output. When the source-receiver configuration is oriented approximately parallel to the solitary wave crests, beam wander, fading, beam splitting and coherence length degradation occurs in a time-dependent manner as the solitary wave packet passes through the environment. Both horizontal refraction of energy and a time-dependent modal source excitation distribution are responsible for these beamforming effects. In cases where source-receiver orientation is not approximately parallel to the wave crests, these effects are substantially reduced or eliminated, indicating that an azimuthally selective perturbation of the acoustic field can be attributed to the wave packet. Modal decomposition of the acoustic field and single mode starting fields are used to infer that, for the source-receiver orientation along the wave crests and troughs, acoustic propagation is predominantly adiabatic. A modal phase speed analysis explains several features associated with the beamformed power.

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

Amplitude and phase variability in acoustic fields are simulated within a canonical shelf-break ocean environment using sound speed distributions computed from hydrodynamics. The submesoscale description of the space and time varying environment is physically consistent with tidal forcing of stratified flows over variable bathymetry and includes the generation, evolution and propagation of internal tides and solibores. For selected time periods, two-dimensional acoustic transmission examples are presented for which signal gain degradation is computed between 200 and 500 Hz on vertical arrays positioned both on the shelf and beyond the shelf break. Decorrelation of the field is dominated by the phase contribution and occurs over 2-3 min, with significant recorrelation often noted for selected frequency subbands. Detection range is also determined in this frequency band. Azimuth-time variations in the acoustic field are illustrated for 100 Hz sources by extending the acoustic simulations to three spatial dimensions. The azimuthal and temporal structure of both the depth-averaged transmission loss and temporal correlation of the acoustic fields under different environmental conditions are considered. Depth-averaged transmission loss varies up to 4 dB, depending on a combination of source depth, location relative to the slope and tidally induced volumetric changes in the sound speed distribution.