Numerical study of Rayleigh-type acoustic streaming based on a three-dimensional incompressible flow model

Rayleigh-type acoustic streaming induced by a plane standing wave in a rectangular parallelepiped is numerically studied on the assumption that the streaming motion is an incompressible flow and induced by the so-called limiting velocity on the outer edge of the acoustic boundary layer on the wall of the rectangular parallelepiped. Solving the three-dimensional incompressible flow equations with a standard finite difference scheme, we show that the streamline indicates chaotic behaviors even when the streaming velocity field converges to a time-independent state (steady flow) for moderate Reynolds numbers. Based on the result, we can discuss an efficiency of mixing by the time-independent Rayleigh-type acoustic streaming motions in three-dimensional boxes.