Rayleigh streaming at large Reynolds number and its effect on shear flow

Abstract

A fluid contained between two parallel walls, one of which is at rest and the other moving in the longitudinal direction with a constant velocity, is examined when a standing sound wave is imposed in the transverse direction. Vortical acoustic streaming appears in the region between the walls. The streaming is not affected by the main flow. A qualitative analysis is presented for the Navier–Stokes equations governing the steady-streaming component of the motion. The study considers the case of flow with high streaming Reynolds number and makes an explicit determination of the vorticity in the inviscid core region. The effect of the streaming upon the shear flow in the longitudinal direction is then analysed asymptotically. A periodic structure of the wall shear stress in the transverse direction is detected in which vast areas of vanishing wall shear stress alternate with narrow regions where it increases significantly. A relation expressing the mean wall shear stress in terms of the streaming Reynolds number is derived. Results obtained show that acoustic streaming results in a marked enhancement of the mean wall shear stress at the walls.