Theory of the backscattering of sound by phase-matched nonlinear interaction

The nonlinear interaction of noncollinear acoustical waves is considered. C onditions of the resonant backscattering of one wave from the lattice produ ced by the other two are formulated in analogy with the four-wave mixing kn own in optics. The efficiency of the phase-matched interaction of acoustica l waves is calculated in the resonant approximation for a gas media. Such a pproximation is constructed on the basis of the expansion of the sound equa tions preserving up to cubic terms. The amplitude of the backscattered wave is expressed as the product of the efficiency, the amplitudes of three wav es,the wave number of the backscattered wave, and the size of the region of interaction. Such backscattering, is proposed as an acoustical remote prob e. The distance to the interaction region and the amplitude of initial Wave s are limited by nonlinear degradation of waves due to the second-order non linearity. For acoustical waves with wave number 10 m(-1), sources of size 1 m, and about 100 m to the interaction region, the amplitude of the backsc attered wave can be about 10(-10) of the atmospheric pressure. At the detec tion with a sigal-to-noise ratio about of 10, the resolution of such method on the wind velocity may be about 1 m/s. (C) 1999 Acoustical Society of Am erica. [S0001-4966(99)04103-X].