Acoustic streaming about a cylinder in orthogonal beams

When orthogonal, plane sound waves of the same frequency, wavelength and amplitude, but with phase difference ½π, are incident upon a circular cylinder there is a time-independent streaming about the cylinder which is in the form of a potential vortex separated from the cylinder by a thin, viscous Stokes layer. As the amplitude of the waves in one of the beams decreases, an additional viscous boundary layer is involved until, when the amplitude is sufficiently small, this flow structure is destroyed as fluid erupts from the boundary layer. In the limit of a single beam it is known that this eruption results in opposing jets perpendicular to the wavefronts of the oncoming wave.