Normal-mode propagation in slowly varying ocean waveguides

Abstract

Acoustic propagation in a slowly varying ocean waveguide can be represented by a set of propagating modes. It is shown that for general slowly varying ocean waveguides, normal modes can be defined in the usual sense of classical mechanics: Normal modes are described by independent differential equations and do not exchange energy. Such modes have also been called intrinsic modes. The derivation is a perturbation method based on the existence of a small parameter ε characterizing the horizontal rate of variation of the waveguide. The expansion is analogous to the Rytov approximation of wave propagation in random media. Uncoupled normal modes (intrinsic modes) are found as perturbation of the local modes. The first-order result is a depth-dependent phase change such that each mode conserves its energy flux as it propagates. An equivalent result is obtained by introducing a nearly orthogonal curvilinear coordinate system in which the Helmholtz equation is separable. The terms of the next order (ε2) show that at this order there is still no coupling. The two solutions are equivalent, and reduce to the exact solution for the wedge problem. Coupled- (local) mode theory is also recovered by doing the proper expansion in the small parameter ε. Comparisons are made with the numerical solution of the ASA benchmark problems. The approximate normal modes effectively sum the terms due to coupling and demonstrate that the concept of coupled modes, with its implication of energy exchange, can be misleading.