Inclusion of continuum effects in coupled-mode theory using leaky modes

Abstract

A difficulty with coupled-mode algorithms for acoustic propagation in sloping, shallow-water regions is properly including the modal continuum. The disadvantage of the standard false-bottom approach is that a large number of modes are needed to represent the continuum, which makes the coupled-mode solution less practical. A leaky mode decomposition requires significantly fewer modes to represent the continuum. However, because the leaky modes are not bounded in the lower half-space, the overlap integrals involved in computing the coupling coefficients are undefined. In addition, the branch line integral, which is not included in the usual coupled-mode formalism, can become significant as modes undergo the transition between being trapped and being leaky. In this work, the approach of inserting a small attenuation gradient in the lower half-space is taken. The half-space gradient makes the mode functions have Airy-function solutions, eliminates the branch cut, replaces it by a series of modes, and makes the leaky modes well behaved at infinite depth. Using the differential form of the coupled-mode equations, overlap integrals can be computed analytically using well-known formulas for Airy functions. The accuracy and efficiency of the approach is evaluated using the ASA benchmark wedge problem as a test case. [Work supported by ONR.]