A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides

Abstract

In this paper, a stepwise coupled-mode model with the use of the direct global matrix approach is proposed. This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry. With the use of the direct global matrix approach, this method is numerically stable. In addition, by introducing appropriately normalized range solutions, thismodel is free from the numerical overflow problem. Furthermore, we put forward source conditions appropriate for the line-source problem in plane geometry. As a result, this method is capable of addressing the scenario with a line source on top of a sloping bottom. Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column. The numerical simulations indicate that the proposed model is accurate, efficient, and numerically stable. Consequently, this model can serve as a benchmark model in range-dependent propagation modeling. Although this method is verified by an ideal wedge problem in this paper, the formulation applies to realistic problems as well.