Interaction of Stokes boundary layer flow with a sound wave

We analyze the interaction of a standing sound wave with the flow generated by the oscillation of a plate in its own plane (Stokes second problem). Th e sound wave acts in the direction transverse to the plate and it is consid ered that the plate oscillation and the sound wave have the same frequency but a nonzero relative phase. The sound wave induces a modification of the axial velocity that consists of two parts, an oscillation with twice the fr equency of the plate oscillation and a steady streaming that persists beyon d the Stokes boundary layer, resulting in a double boundary layer structure . This mechanism for generating steady streaming differs from those studied previously in the literature. The relative phase of the two oscillatory mo tions determines the direction of the net flow. The direction of the steady streaming far away from the plate, coincides with the direction of the dis placement of the plate at the moment of maximum compression and is proporti onal to the velocity of the plate at this moment. (C) 2001 American Institu te of Physics.