Geometry of sand ripples due to combined wave-current flows

Laboratory data on sand ripple spacing due to combined wave-current motion are collected to examine the validity of the empirical formula proposed by Tanaka and Shuto (1984). Data from Gray et al. (1991) and from Van Rijn et al. (1993) showed considerable discrepancy from the formula. The discrepancy can partly be attributed to insufficient consideration of the grain size effect in the previous study. Furthermore, incorrect evaluation of the orbital diameter due to wave motion, which was pointed out by Christoffersen and Jonsson (1985), can be another reason for the discrepancy. A new formula for the spacing of wave-current-induced sand ripples is derived. The agreement between the measurement and the prediction can be much improved as compared with the previous formula. The full-range equation for the wave-current friction coefficient proposed by Tanaka and Thu (1994) is applied in the formulation of steepness of sand ripples. Empirical equations for pure wave ripples can tentatively be used for estimating the steepness of sand waves.