Scattering of Sound by Internal Wave Currents: The Relation to Vertical Momentum Flux

Abstract

Internal waves scatter sound by two related perturbations: 1) those associated with vertical particle displacements ?(x, y, z, t) in the presence of a vertical gradient of (potential) sound speed (δc = ??zcp); and 2) those associated with horizontal particle velocities u(x, y, z, t). The combined fractional perturbation in propagation velocity is δc/c + u/c. The second term, generally neglected, introduces a nonreciprocity when source and receiver are interchanged. Nonreciprocity is expected to be relatively small except for transmission along a deep downward loop. The principal internal wave contribution to nonreciprocity is from inertial frequencies. The sum and difference of reciprocal travel times are a measure of ? and u, respectively, along the ray path,, the quadrature spectrum of reciprocal travel times is related by an integral equation to the spectrum of the momentum flux ??u?. Precise measurements of nonreciprocity could provide an estimate of the vertical momentum flux in an internal wave field.