Oscillatory Flows over a Permeable Wavy Boundary

Abstract

ABSTRACTIn this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.