Coupled-mode sound propagation in a range-dependent, moving fluid.

Full-field acoustic methods for current velocity inversion require accurate and efficient mathematical models of sound propagation in a range-dependent waveguide with flow. In this paper, an exact coupled-mode representation of the acoustic field is derived. To account for the physics of the problem, normal modes in a corresponding range-independent waveguide are chosen as the local basis. In the absence of currents, mode shape functions form a complete orthogonal basis. This property is heavily used in coupled-mode theories of sound propagation in motionless fluid. Unlike in the motionless case, however, vertical dependencies of acoustic pressure in individual normal modes are not orthogonal in the presence of currents. To overcome this difficulty, linearized equations of hydrodynamics are rewritten in terms of a state vector. Its five components are expressed in terms of acoustic pressure and particle displacement due to the wave. Orthogonality of the state vectors corresponding to individual normal modes is established. Coupled differential equations are derived for range-dependent mode amplitudes, leading to a remarkably simple result. The mode-coupling equations have the same form as those known for the motionless case, but of course the values of the mode-coupling coefficients differ as long as the range dependence of the flow velocity contributes to mode coupling in addition to the range dependence of sound speed and fluid density. The mode-coupling formulation is verified against known coupled-mode equations for certain limiting cases and an exact analytic solution of a benchmark problem.