The continuation of the normal mode solution of the underwater acoustic wave equation

Abstract

Conditions are established that support the continuation of the usual normal mode, separation of variables, solution of the reduced wave equation in a lossy underwater acoustic waveguide. The conditions exclude the existence of generalized eigenfunctions that occur when the loss is large enough to cause the eigenvalues of the lossless problem to coalesce. The existence of generalized eigenfunctions substantially complicates the normal mode solution for the acoustic field in the waveguide, so conditions that preclude their existence are of practical interest. The methods used to establish the conditions are taken from analytic perturbation theory. Examples are given to show how to use the conditions.