A Three-Dimensional Energy Flux Model for Acoustic Propagation in the Ocean

This paper extends energy flux methods to handle three-dimensional ocean acoustic environments, the implemented solution captures horizontally refracted incoherent acoustic intensity, and its required computational effort is predominantly independent of range and frequency. Energy flux models are principally derived as incoherent solutions for acoustic propagation in bounded waveguides. The angular distribution of incoherent acoustic intensity may be derived from Wentzel-Kramers-Brillouin modes transformed to the continuous angular domain via the ray-mode analogy. The adiabatic approximation maps angular distributions of acoustic intensity as waveguide properties vary along a range-dependent environment, and the final solution integrates a modal intensity kernel over propagation angles. Additional integration kernels can be derived that modulate the incoherent field by specific physical wave phenomena such as geometric spreading, refractive focusing, and boundary attenuation and interference. This three-dimensional energy flux model is derived from a double-mode-sum cross-product, is integrated over solid-angles, incorporates a bivariate convergence factor, accounts for acoustic energy escaping the computational domain through transparent transverse boundaries, and accumulates bottom attenuation along transverse cycle trajectories. Transmission loss fields compare favorably with analytic, ray tracing, and parabolic equation solutions for the canonical ASA wedge problem, and three-dimensional adiabatic ray trajectories for the ideal wedge are demonstrated.