Dynamics and geometry of wave‐generated ripples

Abstract

Semi‐empirical formulae for the size and shape of sand ripples are derived from an analysis of the water and sediment motion over a rippled bed in oscillatory flow. Simple physical arguments show that ripple steepness should be a function of the nondimensional shear stress θ′ and the angle of repose of the bed material. All available data seem to support this. The mechanisms that determine the ripple length are very complex, and at least four nondimensional parameters are important. However, for practical purposes the ripple length is well determined by the mobility number ψ. ψ is essentially the ratio of the water velocity amplitude to the sediment settling velocity. Both ripple length and ripple height are shown to depend mainly on ψ, when only quartz sand and natural wave periods are considered. The derived formulae apply well to the full range of flow conditions, where ripples occur. Natural ripples obey essentially the same rules as laboratory ripples; however, they are generally shorter and flatter owing to the irregularity of natural waves.