Sand ripples under sea waves Part 1. Ripple formation

Abstract

In the present paper we formulate a predictive theory of the formation of sand ripples under sea waves. The theory is based on a linear stability analysis of a flat sandy bottom subject to a viscous oscillatory flow. The conditions for decay or amplification of a bottom perturbation are determined along with the wavelength of the most unstable component as a function of the Reynolds number of the flow and of the Froude and Reynolds numbers of the sediments. A comparison between theoretical findings and experimental data supports the validity of the present theory. An analytical solution for viscous oscillatory flow over a small-amplitude wavy bottom is determined for arbitrary values of the ratio r between the amplitude of fluid displacement and the wavelength of bottom waviness. Previous works by Lyne (1971) and Sleath (1976), who considered small or large values of r , are thus extended.