Two-Way Coupled-Mode Solutions in the Complex Horizontal Wavenumber Plane

Abstract

A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am. 111 (2002) 1623-1643, referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am. 96 (1994) 1741-1747. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

Rough surface scattering in a Born approximation from a two-way coupled-mode formalism

“…The off-diagonal scattering kernel components derived thereby are equivalent to the off-diagonal components of the MJ scattering kernel with proper dimensions. This derivation for the scattering kernel is valid for an arbitrary horizontal layering profile 2,3 and avoids the calculation of a reflection coefficient that is extraneous to a reverberation model constructed with propagated fields determined from modes that already incorporate reflection effects.…”

Derivation of energy loss via coupled modes

“…A variety of coupled mode effects in underwater acoustic propagation can be examined by numerical calculations for simplified environments with a full coupled mode model. [1][2][3] Calculations with the Problem I environment for the Reverberation Modeling Workshop I (RMWI) have been performed to examine some of these effects. [4][5][6] Another way to examine coupled mode effects is to produce analytic approximations for some of the properties of the numerical calculations, e.g., reverberation levels from a Born approximation.…”