Predicting ripple geometry and bed roughness under combined waves and currents in a continental shelf environment

Abstract

Waves, current and seabed response data collected by an instrumented tripod deployed on the Scotian Shelf during the winter of 1993/94 are analyzed to derive a ripple predictor for combined flows and to evaluate the applicability of existing ripple- and bedload-roughness algorithms under combined waves and current. Wave-dominant ripples developed during storms were generally higher and steeper than current-dominant ones. The ratio of the skin-friction wave shear velocity to that of the steady current, u ∗ ws /u ∗ cs , can be used to define the various types of ripples under combined flows. By comparing the measured ripple geometry and the predictions by existing ripple predictors, the wave-ripple predictors of Nielsen (1981), and Grant and Madsen (1982) are found to over-predict ripple height and ripple roughness for combined flows under the conditions of the present study. These methods also neglect the enhancement of shear stress at the ripple crest. A new empirical ripple predictor is proposed and it uses the combined shear velocity and the ratio u ∗ ws /u ∗ cs to predict the heights and wavelengths of ripples and their dynamic transition under combined flows. The effect of enhanced shear velocity at the ripple crest is also incorporated for the prediction of ripples in the weaktransport range. A simplified logarithmic profile method and the values of the bedload shear velocity due to the combined grain size and bedload roughnesses are used to evaluate the applicability of various ripple- and bedload-roughness height algorithms under combined flows. While the ripple roughness height algorithm of Grant and Madsen (1982) is found to give good predictions of the total current shear velocity u ∗ c and apparent bottom roughness z 0c, the algorithm of Nielsen (1992), tends to underpredict both parameters. The bedload roughness algorithms of Nielsen (1992) and Li et al. (1997) are both found to give reasonable predictions under combined flows. The total bed roughness height under combined flows can be expressed as k b=2.5 D+27.7 η 2/ λ+170 D( θ cws− θ cr) 0.5.