Multiple existence of steady state solutions of acoustic streaming in a long two-dimensional rectangular box

Abstract

The large amplitude standing wave excited in a resonator induces acoustic streaming of Rayleigh type outside the acoustic boundary layer on the wall of the resonator. The streaming motion with large Reynolds number is examined numerically in relatively long two-dimensional rectangular boxes. The two-dimensional incompressible Navier–Stokes equations with no external force are used as the governing equations for the streaming velocity. The steady velocity component at the outer edge of the acoustic boundary layer, which induces Rayleigh type streaming, is employed as the boundary condition for the Navier–Stokes equations. By using a finite-difference method, the existence of multiple steady state solutions is demonstrated. Some of the numerically obtained flow patterns bear a resemblance to those obtained experimentally. It may be remarked that all the flow patterns induced by the fifth mode standing wave in a relatively long box can be regarded as combinations of those induced by the second mode standing wave in a short box.