Energy characteristics of the passage of a sound wave through regions of stepwise changes in the waveguide cross section

At present time, the theoretical basis for modeling sound propagation in marine waveguides is the analysis of boundary value problems for the Helmholtz equation, while the ocean bottom is an uneven interface between different media and is considered as a set of geological objects with different shapes and structures. The paper presents an analytical solution to the problem of sound propagation by a point source in a waveguide with a stepwise change in the cross section, which is modeled as a cylindrical protrusion or cavity. The velocity potential is constructed in each part of the waveguide decomposition as a series in normal modes, followed by matching the solution at the boundary. To calculate the unknown coefficients of normal modes, the theory of infinite systems of linear algebraic equations is used. The presented solution makes it possible to significantly simplify the study of the most important characteristic of the sound field is the energy flux through the cross section. The paper investigates the energy characteristics of a sound wave in a waveguide having a cylindrical protrusion (or cavity). Examples of numerical implementation are given for problem parameters, which are typical for geophysical waveguides.