Space‐time parabolic equation in horizontal plane for description of non‐stationary horizontal refraction in shallow water.

Abstract

Propagation of the sound signals in inhomogeneous anisotropic shallow water environment is studied. Because the waveguide dispersion shape of the radiated pulse is being changed, waveguide modes have different group velocities and, generally speaking, propagate along different ray paths in the horizontal plane. It can lead to simultaneous redistribution of the sound pulse intensity in the horizontal plane and compression/decompression in time. For a description of the spatial and temporal variation of the traveling pulse, space‐time horizontal rays and space‐time parabolic equation in the horizontal plane are derived using a standard approach used in electrodynamics based on integral non‐local connection between field and response. Non‐stationary parabolic equation (PE) is an extension of the well known approach of vertical modes and PE in the horizontal plane. This equation is analyzed and its solutions are constructed for different models of perturbation: nonlinear internal waves, coastal slope, etc.