Movable bed roughness and current profiles in the presence of irregular waves with an arbitrary angle to currents

The bed roughness k_s and current velocity profiles in the presence of waves with an arbitrary angle θ to currents are studied. It is found that the movable bed roughness is affected by both the wave and the current and only slightly by the angle θ between the wave propagation and the current, and that existing formulae derived in purely oscillatory flows generally fail to predict k_s. In the present study, a new formula which takes account the effect of the wave and the current on the bed roughness is suggested to calculate k_s in combined wave-current flows. With the present formula, the current profiles calculated by the model of You agree satisfactorily with the laboratory data of van Kampen and Nap and Havinga, and the field measurements of Grant and Williams and Drake et al.