### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 4pPA6. Acoustic streaming at high Reynolds numbers in focused sound beams.

**M. F. Hamilton
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Yu. A. Il'inskii
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E. A. Zabolotskaya
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*Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063
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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. Hob(ae ligature)k
(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.]