A variational principle for underwater acoustic propagation in a three-dimensional ocean environment

The problem of determining the sound field due to a point harmonic source in an ocean environment with an arbitrary three-dimensional local variation of field parameters (including irregular interfaces) is studied with the help of a variational principle. The variational principle is established by proving that the Euler–Lagrange equations of a suitable functional coincide with the field equation and the exact boundary and interface conditions of the complete elliptic boundary value problem. The method presented in the paper is a hybrid one, in the sense that the pressure field is represented by modal series expansions in the range-independent region, and a suitable localized expansion in the range-dependent region of the environment. These representations retain full mode coupling and, in conjunction with the variational principle, reduce the problem to a linear system of equations free of any a priori restrictions. It is expected that this system would be efficiently used for the numerical solution of the problem, especially in a shallow water environment and in the low-to-moderate frequency range.