Acoustic streaming at high Reynolds numbers in focused sound beams

Abstract

In experiments reported recently on acoustic streaming in focused sound beams [Starritt et al., Ultrasound Med. Biol. 15, 363 (1989), and Matsuda et al., Advances in Nonlinear Acoustics: 13th ISNA, edited by H. Hobæk (World Scientific, Singapore, 1993), pp. 595–600], the Reynolds numbers for the streaming are of order 100. To model such experiments, nonlinearity in the momentum equation for the streaming velocity should be taken into account. Previous comparisons of theory with measurements of acoustic streaming in focused beams are based on linear equations for the streaming velocity, which are normally valid only for Stokes flows characterized by Reynolds numbers less than unity [Lighthill, J. Sound Vib. 61, 391 (1978)]. The numerical results presented here were obtained with nonlinear inertia terms for the streaming velocity retained in equations that describe the paraxial region of the beam. The primary wave is assumed to be a focused Gaussian beam, with parameters corresponding to the experiments cited above. Inclusion of nonlinearity yields predictions of streaming patterns that are more localized in the focal region, and in closer agreement with experiment, than predictions based on linearized equations for the flow. [Work supported by Schlumberger, NSF, and the Office of Naval Research.]