An empirical model for the development and equilibrium morphology of current ripples in ®ne sand

A ̄ume study on the development and equilibrium morphology of current ripples in ®ne sand (D50 ˆ 0á238 mm) was performed to extend an empirical model for current ripple stability in 0á095 mm sand to larger grain sizes. The results of the ̄ume experiments agree with the very ®ne sand model that current ripple development from a ̄at bed is largely independent of ̄ow velocity. At all ̄ow velocities, ripples evolve from incipient, through straight, sinuous and non-equilibrium linguoid, to equilibrium linguoid plan morphology. The time needed to achieve an equilibrium linguoid plan form is related to an inverse power of ̄ow velocity and ranges from several minutes to more than hundreds of hours. Average equilibrium height and length are 17á0 mm and 141á1 mm respectively. These values are about 20% larger than in very ®ne sand. Equilibrium ripple height and length are proportional to ̄ow velocity near the stability ®eld of dunes. In the same velocity range, a characteristic grouping of ripples with smaller ripples migrating on the upstream face of larger ripples was observed. Bed-form development shows a conspicuous two-phase behaviour at ̄ow velocities < 0á49 m s. In the ®rst phase of development, ripple height and length increase along an exponential path, similar to that at higher ̄ow velocities, thus reaching intermediate equilibrium values of 14á8 mm and 124á5 mm respectively. After some time, however, a second phase commences, that involves a rapid increase in bed-form size to the typical equilibrium values for 0á238 mm sand. A comparison with literature data shows that the results obtained for 0á238 mm sand agree reasonably well with other ̄ume studies at similar grain size. Yet considerable variability in the relationships between ripple dimensions and ̄ow strength ensues from, among others, underestimation of equilibrium time, shallow ̄ow depths and differences in sediment texture.