Three-dimensional analytical solution and numerical solution in a penetrable wedge-shaped waveguide

Abstract

An exact analytical solution for three-dimensional sound propagation excited by a point source in a penetrable wedge-shaped ocean is first presented in this paper. Although Deane and Buckingham have proposed an analytical solution for the acoustic field in the water of a penetrable wedge (Journal of the Acoustical Society of America, 1993, 93(3): 1319∼1328), the analytical solution is not complete. It is only applicable for sea water not for the seabed, hereafter called bottom. This paper presents an analytical field solution which not only applies to sea water but also the bottom. The analytical solution is obtained by using the method of source images. For the acoustic field in the water of a penetrable wedge, only acoustic reflection needs to be considered. All the source images on a circle centered on the wedge apex need to be involved in the computation. However, for the acoustic field at the bottom of a penetrable wedge, both acoustic reflection and acoustic refraction need to be considered. Only the source images above the bottom on a semicircle need to be involved in the computation. The analytical solution in the whole sea area can be obtained based on the plane wave reflection and refraction principles. In addition, a three-dimensional numerical model based on the wavenumber integration method is also presented and implemented in an unconditionally stable direct-global-matrix coupled-mode method. Afterwards, the three-dimensional numerical model is applied to sound propagation excited by a point source in a benchmark wedge waveguide. The numerical solutions from the three-dimensional model agree well with the analytical solutions in the benchmark wedge waveguide. Consequently, the present three-dimensional model is validated through the analytical solutions to the benchmark wedge problem.