Turbulent acoustic streaming with large Reynolds number and its effects on the thermal conduction and mixing

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Acoustic streaming is a mean mass flow induced by the nonlinear effect of acoustic waves. It has been expected that turbulent acoustic streaming can enhance the thermal conduction, mixing, and stirring of materials in vessels. The lack of a full understanding of the physical characters of acoustic streaming with large Reynolds number prevents the development of such technologies. In the present study, we have theoretically and numerically investigated acoustic streaming with large Reynolds number induced by large amplitude resonant gas oscillations in a closed tube. The method of theoretical analysis is based on the singular perturbation. The numerical methods are a high-resolution upwind TVD scheme and a standard MAC method.The main results can be summarized as follows:(1) We have examined the one-dimensional oscillations, which is of the most fundamental importance in our problem. We have shown that the amplitude modulation occurs in an initial transient state, and that the temperature in the gas is raised by the heat production due to the shock waves.(2) The streamlines of acoustic streaming are distorted by the shock waves.(3) A vortex doubling bifurcation has been demonstrated by a large scale numerical simulation.(4) We have numerically shown that a bifurcation of steady state solution of acoustic streaming in a 2-dimensional box creates a pair of steady state solutions, which lose the symmetry of the original solution. The streaming motion after the bifurcation is a large scale circulatory motion in the box. This means that acoustic streaming with large Reynolds number may be useful for thermal conduction, mixing, and stirring of materials in vessels.