Asymptotic stepwise coupled modes for horizontally-variable acoustic media

Abstract

Efficient and accurate mathematical codes for the prediction of underwater sound propagation are a critical component of SONAR system development and operation. The goal of the research presented herein is to develop, implement, and verify an efficient and rigorous coupled-mode solution for acoustic wave propagation in shallow water range-dependent environments. A theoretical framework involving a range-expanded inner product for capturing the coupling between modes as they propagate through a horizontally-variable medium is presented. This framework includes a novel discretization of the range-dependent acoustic medium. A difference equations approach, which implements the inner product to account for non-adiabatic energy transfer between modes, is used to recursively compute reflection and transmission coefficients throughout the discretized environment. Increased efficiency is gained in the method due to the ability to compute coupling via closed-form algebraic expressions and in the application of asymptotic analysis to simplify the transmission and reflection coefficients. Results will be shown for a sample of waveguides with horizontally-variable bottom depth, along with comparable results from R. Evans’ COUPLE model and an FEM solution produced by ARL-UT. [This work was funded by the Naval Undersea Warfare Center, Newport Rhode Island.]