An analytical solution is derived for the acoustic streaming generated by two orthogonal standing waves in a fluid confined between two plane rigid walls. It is assumed that the standing waves have the same frequency but, in general, are out of phase. The main restriction is that the boundary layer thickness is much smaller than the acoustic wavelength. It is shown that the acoustic streaming gives rise to vortices in which fluid particles, when moving between the walls, are rotating about axes perpendicular to the walls. The location, the form, the sense of rotation of the vortices and the vortex strength are governed by the phase shift between the driving waves.
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