Dynamic Friction Coefficient in Formulas of Bed-Load Transport Induced by Waves over Vortex Orbital Ripples

Empirical formulas for the computation of bed sediment transport induced by wave propagation over sand ripples often depend on, among other parameters, the dynamic friction coefficient, mu(d), of the sand grain motion. Here, a new approach is presented for the determination of mu(d) based on the physics of the interaction between flow and sediment transport. Specifically, the correlation of mu(d) to the wave, ripple, and sand grain characteristics was obtained using coupled numerical simulations of the flow over the rippled bed, the bed-load transport, and the bed morphology evolution. Flow results were obtained by two different numerical methods, one for wave boundary layer flow and one for purely oscillatory flow, both based on the solution of the Navier-Stokes equations. The bed-load transport rate, which drives the bed morphology evolution, was computed using three different empirical formulas. The value of mu(d) that leads to an equilibrium of the rippled bed profile after many wave periods was found to depend almost linearly on (Lr/a(o)).(hr/a(o)), where, L-r is the ripple length, h(r) is the ripple height, and a(o) is the wave orbital motion amplitude.