Adiabatic approximate solution for the problem of sound propagation in shallow sea with a broadening underwater canyon

Abstract

The problem of sound propagation in a shallow-water waveguide with a broadening underwater canyon is considered. The acoustical field in the waveguide is expressed in the form of a modal expansion. Under the adiabatic assumption for the sound propagation the equations for modal amplitudes are decoupled and then solved analytically by the Fourier method in cylindrical coordinates. In turn, the angular eigenfunctions are computed using their representation in the form of the standard Fourier series. A numerical example is presented in order to visualize the obtained expression for the acoustical field. The proposed solution can be used as a benchmark for the numerical methods of the 3D sound propagation modeling.