RAYLEIGH STREAMING AT LARGE REYNOLDS-NUMBER AND ITS EFFECT ON SHEAR-FLOW

A fluid contained between two parallel walls, one of which is at rest and the other moving in the longitudinal direction with a constant vel ocity, is examined when a standing sound wave is imposed in the transv erse direction. Vortical acoustic streaming appears in the region betw een the walls. The streaming is not affected by the main flow. A quali tative 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 explici t determination of the vorticity in the inviscid core region. The effe ct of the streaming upon the shear flow in the longitudinal direction is then analysed asymptotically. A periodic structure of the wall shea r stress in the transverse direction is detected in which vast areas o f vanishing wall shear stress alternate with narrow regions where it i ncreases significantly. A relation expressing the mean wall shear stre ss in terms of the streaming Reynolds number is derived. Results obtai ned show that acoustic streaming results in a marked enhancement of th e mean wall shear stress at the walls.