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

Abstract

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 for the corresponding 2-D problem. To account for the physics of the problem, normal modes in a corresponding range-independent waveguide are chosen as the local basis. Unlike the motionless case, vertical dependencies of acoustic pressure in individual normal modes are not orthogonal in the presence of currents. To overcome this difficulty, a five-dimensional state vector is introduced. Orthogonality of the state vectors corresponding to individual normal modes is established. In terms of the state vector, the set of linearized equations of the hydrodynamics becomes a single differential equation of the first order with respect to the range coordinate. By using the orthogonality, coupled equations are derived for range-dependent mode amplitudes. The resulting mode-coupling equations have the same form as those known for motionless case, but values of mode-coupling coefficients differ. The contributions to mode coupling from horizontal gradients in the sound speed, density, and flow velocity are isolated and analyzed. [Work suported by NSERC and ONR.]