Migrating sea ripples

Ripple formation under sea waves is investigated by means of a linear stabi lity analysis of a hat sandy bottom subject to the viscous flow which is pr esent in the boundary layer at the bottom of propagating sea waves. Nonline ar terms in the momentum equation are retained to account for the presence of a steady drift. Hence the work by Blondeaux is extended by considering s teeper waves and/or less deep waters. Second order effects in the sea wave steepness are found to cause neither destabilizing nor stabilizing effects on the process of ripple formation. However, because of the presence of a s teady velocity component in the direction of wave propagation, ripples are found to migrate at a constant rate which is predicted as function of sedim ent and wave characteristics. The analysis assumes the flow regime in the b ottom boundary layer to be laminar and the results are significant for ripp les at the initial stage of their formation or for mature ripples of small amplitude (rolling-grain ripples). A comparison of the theoretical findings with laboratory experiments supports the reliability of the approach and o f the theoretical results. (C) 2000 Editions scientifiques et medicales Els evier SAS.