Threshold for Ripple Formation on Artificially Roughened Beds: Wave-Flume Experiments

Abstract

The lack of systematic studies of the influence of bottom irregularities on ripple initiation led to a series of wave-flume experiments with the purpose of exploring a general relationship. Three types of sand beds with different degrees of roughness were prepared for the experiments: flat, notched, notch-mounded beds. Three kinds of well-sorted sands with different diameters were used for the bed material: fine, medium, and coarse sands. With combinations of waves, water depth, sand, and bed roughness, 248 experimental runs were carried out. Data were analyzed considering (1) the mobility of sediment, expressed in terms of the mobility number, M, (2) the degree of bed roughness, represented by the Reynolds number, Re, and (3) the asymmetry of flow field due to nonlinearity of waves, represented by the relative water depth, kh (= 2πh/L; h = water depth and L = wavelength). The result showed that the threshold for rippling is described by M = 2 A exp B, where A = 5.7 (3.79/(kh 0.65) − 1) and B = −8 × 10−4 Re. It was found that the threshold decreases with increase in bed roughness and attains constant value with further increased bed roughness. The threshold also decreases as the flow field becomes more symmetric. Comparison between available field data and the present findings shows that the threshold on a well-roughened bed, M = 2, defines the critical condition for ripple formation in the natural environment.