Oscillating turbulent flow over very rough surfaces

The forces on the seabed in shallow water under waves influence near-shore transport processes. However, the actual nature of these forces is not yet fully understood. Sleath [1987] simultaneously measured horizontal shear force per unit area and Reynolds stress in oscillating turbulent flow over granular beds with the striking result that maximum Reynolds stress was significantly less than total shear force per unit area of bed. Trying to explain these measurements, we use a formulation which considers two kinds of flow perturbations, namely turbulent fluctuations and some disturbances due to boundary irregularities. The resulting spatially averaged Reynolds equations contain in particular two terms which do not appear in the smooth bed case: the force due to the mean momentum flux for boundary disturbances, here called ''form-induced stress,'' which owes its existence to the vorticity of the disturbed motion, and the force exerted by the roughness elements on the fluid. The ''jet regime'' as introduced by Gimenez-Curto and Corniero [1993] for steady flow is extended to oscillatory flow. In this regime, pressure drag on roughness elements is the fundamental force acting on the boundary, and form-induced stress due to vorticity generated by flow separation from bed irregularities becomes the leading stress, thus providing an explanation for Sleath's measurements by means of a physical mechanism which was already envisaged by Longuet-Higgins [1981] for two-dimensional rippled beds. A simple expression is derived for the friction coefficient which is subsequently compared with extensive series of measurements in the laboratory for granular beds as well as for rippled surfaces, showing an excellent agreement.