Current and current shear effects in the parabolic approximation for underwater sound channels

Abstract

The effect of currents on the acoustic pressure field in an underwater sound channel is investigated. Based on fundamental fluid equations, model equations are formulated for sound pressure while including nonuniform currents in the source–receiver plane. Application of parabolic-type approximations yields a collection of parabolic equations. Each of these is valid in a different domain determined by the magnitudes of current speed, current shear, and depth variation of sound speed. Under certain conditions, it is possible to interpret current effects in terms of an effective sound speed. Using this effective sound speed in an existing numerical code, we examine sound speed in a shallow water isospeed channel with a simple shear flow and a lossy bottom. It is found that even small currents can induce very substantial variations in relative intensity. The degree of variation depends upon current speed, source and receiver geometry, and acoustic frequency. Particular emphasis is placed on intensity-difference predictions in reciprocal sound transmissions in the presence of an ocean current.

Geometric sound propagation through an inhomogeneous and moving ocean: Scattering by small scale internal wave currents

“…While some general treatments exist ͑Uginčius 1965͑Uginčius , 1972Thompson 1972;Godin and Voronovich, 2004͒, the ocean acoustic literature on the theory of the effects of currents on sound propagation has somewhat overemphasized cases in which the current is only a function of depth ͑Blokhintzev 1946; Keller 1954;Stallworth and Jacobson 1972a, b;Franchi and Jacobson 1972;Robertson et al 1985͒ or only the observable of travel time is treated in detail ͑Munk, Worcester, and Wunsch 1995͒. In the theory of ocean acoustic scattering, established work in this area ͑Flatte et al. 1979;Colosi et al 1999 and references therein͒ has not rigorously evaluated the effects of ocean currents on acoustic propagation, and the focus has been almost entirely on sound speed fluctuations from the Garrett-Munk internal wave model ͑Munk 1981͒.…”

A wide angle and high Mach number parabolic equation

“…This approach is of limited use for advected acoustic waves. Various approximate parabolic equations [2][3][4][5][6][7][8][9][10][11] have been derived for this problem using the assumptions of low Mach number and narrow propagation angle, which are of limited validity for atmospheric acoustics problems. In this paper, we derive a parabolic equation solution that does not require these assumptions.…”

Numerical Analysis of the Effect of Mesoscale Eddies on Seismic Imaging

“…Consequently, terms of O Mn ð Þ will be negligibly small compared to M (ROBERTSON et al, 1985), then Eq. (9) reduces to…”

“…This is necessary because small currents may give rise to rather large current shears (ROBERTSON et al, 1985). Thus, the current gradient can be expressed as…”

“…However, for the analytic eddy model in our paper, the relation between the density and the sound speed of mesoscale eddies are much more complicated (HEN-RICK et al, 1977). Further, as mentioned above, in mesoscale eddies the water rotates with a nonuniform velocity, so a wave equation including nonuniform current effect is more desirable (ROBERTSON et al, 1985). In this paper, to investigate the effect of mesoscale eddy, an appropriate partial differential equation is derived for the acoustic pressure field while including the density variations and nonuniform currents in the eddy.…”