A Normal Mode Method of Solution for Deep Ocean Propagation

Abstract

The sound velocity distribution in the ocean is considered a function of depth only. The ocean model is separated into three layers. The surface and bottom layers are represented by linear profiles while the middle layer is assumed to have a velocity profile described by a polynomial. The bottom layer is unbounded, and therefore only one solution to the wave equation is needed to describe the field in it. The bounded surface and middle layers require two solutions of the wave equation to depict the “outgoing” and “uncoming” waves. The solutions for the linear regions are in terms of Bessel functions whereas the field in the middle region is defined by two infinite series. After application of the boundary conditions, the constants of the solutions can be determined, and a normal mode evaluation of the solution is given. For typical profiles off the coast of Eleuthera, the integral representation of the solution is found to be rapidly convergent. The Gaussian approximate method for numerical evaluation is used for evaluation of the field.