Propagation Speed and Attenuation Coefficient for Plane Coherent Acoustic Waves in a Turbulent Medium

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Abstract
The results of numerical calculations of the propagation speed and attenuation coefficient for plane coherent acoustic waves propagating in a weakly stochastic fluid medium, based on equations derived previously, are presented. Two special cases are considered: waves in a randomly inhomogeneous fluid at rest, and waves in isentropic irrotational turbulent flow. In each case the medium is assumed to be statistically homogeneous and isotropic, and is assumed to have an exponential correlation function. The results for both cases indicate that the propagation speed of the coherent wave is less than the average sound speed of the medium; also that the attenuation coefficient increases, whereas the propagation speed decreases, with increasing wave frequency. The results obtained for waves propagating in motionless sea water (at 15°C, 1 atm, 35‰ salinity) are compared with corresponding results obtained by basing the analysis on the scalar wave equation. It is concluded that, in underwater acoustics, basing the analysis of the coherent wave in a quiescent medium on the scalar wave equation or stochastic Helmholtz equation, generally yields accurate results for the attenuation coefficient, but may lead to considerable error in the calculation of the propagation speed.

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