Abstract:

In an earlier presentation [Hamilton et al., J. Acoust. Soc. Am. 97, 3376(A) (1995)], a theoretical model for acoustic streaming at high Reynolds numbers (based on streaming velocities) in thermoviscous fluids was used for analytical and numerical predictions based on the assumption of weakly nonlinear focused Gaussian beams. Here, numerical calculations of streaming are presented for radiation from circular pistons, both focused and unfocused, and at amplitudes for which shock formation occurs. The forcing function for the streaming equations is evaluated with time-domain numerical solutions of the nonlinear parabolic wave equation. Effects of thermoviscous dissipation on the acoustic waveforms, and in particular on shock structures, are taken into account explicitly. The calculations provide a consistent description of acoustic streaming generated in real fluids by sound beams at moderate amplitudes, either with or without shocks. Because the shocks are not considered to be discontinuous features of the solutions, uniformly valid predictions of streaming are obtained in the transition region encompassing the birth and death of shocks amid the competing effects of dissipation and diffraction. The model accommodates both continuous and pulsed sources. Comparisons are made with experiments reported in the literature. [Work supported by the Office of Naval Research.]