Effects of coupling of forward-backward modal components on continental slope ocean environment.

Abstract

An exact solution to the two-dimensional (2-D) Helmholtz equation in an inhomogeneous environment may be expressed as a superposition of forward and backward traveling modes. The modal amplitudes of both components are generally coupled in the same manner that positron and electron amplitudes are coupled in the presence of an electric field, resulting in Zitterbewegung for the electron. In ocean acoustics, an accurate treatment of such coupling can become important over long propagation distances across continental slope environments with inhomogenities in either the surface or bottom boundary conditions, the volume of the water column, or both. The coupled integral equation for the range-dependent modal amplitudes is decomposed into the forward and backward modal components using the asymptotic boundary conditions of Green’s function operator. In addition to an exact treatment to the coupling, a perturbation approach is introduced to include the forward-backward coupling effects within a one-way integral equation. The perturbations are introduced via a channel elimination approach that results in a nonlocal optical potential or effective interaction. The nature of this potential and the perturbation convergence criteria are examined for the case of bottom sand dunes and internal waves. [Work supported by the ONR.]