Mixing efficiency of sediment and momentum above rippled beds under oscillatory flows

While the nature of the suspended load above steep, wave-induced, sand ripples is of practical importance, it also raises intriguing questions about the relative mixing efficiencies of sediment and momentum above the seabed. It has been widely accepted that the mixing efficiency of sediment is substantially greater than that of momentum. But, hitherto, this has not been explained clearly in terms of the underlying, detailed physical mechanisms which revolve around the generation and ejection of sediment-laden vortices at the ripple crest, and their subsequent advection by the flow. A two-dimensional discrete-vortex, particle-tracking research model, with the parameter settings corresponding to a well-documented laboratory experiment, is used here to represent these processes. Both the modelled and also experimental flow and concentration fields are described in detail, together with the horizontally (ripple-) averaged fields, and the cycle-mean, ripple-averaged fields. From these considerations, the ratio (β) of the sediment diffusivity to the eddy viscosity, or the inverse of the Schmidt number, is then determined. It is found that β is larger than unity, in fact between 1.3 and 3.1 for two different computational approaches (based on harmonics and exponential fitting) for the model and data. These values for β agree well with previous results reported in the literature. This research elucidates, from fundamental principles related to spatio-temporal correlations between concentration and velocity, the improved efficiency of sediment mixing compared with momentum mixing in the vortex layer above rippled beds and its key role in determining suspension profiles in such flows