An energy-conserving one-way coupled mode propagation model

The equations of motion for pressure and displacement fields in a waveguide have been used to derive an energy-conserving, one-way coupled mode propagation model. This model has three important properties: First, since it is based on the equations of motion, rather than the wave equation, instead of two coupling matrices, it only contains one coupling matrix. Second, the resulting coupling matrix is anti-symmetric, which implies that the energy among modes is conserved. Third, the coupling matrix can be computed using the local modes and their depth derivatives. The model has been applied to two range-dependent cases: Propagation in a wedge, where range dependence is due to variations in water depth and propagation through internal waves, where range dependence is due to variations in water sound speed. In both cases the solutions are compared with those obtained from the parabolic equation (PE) method.