The stability of ripples and dunes

Abstract

The stability of ripples and dunes in flows of finite depth are investigated for the linear, small-amplitude case and also for the more realistic finite-amplitude situation. For the former perturbation approach is taken, leading to the general result that, without the inclusion of some lag between the sediment transport rate and the boundary shear stress, all wavelengths are unstable. This results from an upstream shift in the stress relative to the bedform, leading to deposition at the crest. By assuming a realistic lag based on the mechanics of bed load transport, a fastest growing wave at ripple-scales results: similarly, if suspended sediment were included, longer lags result and a dune-scale instability could result. Some investigators have invoked a gravitational effect, arguing that sediment transport is enhanced downslope and retarded upslope. This creates an effective downstream shift in the transport rate and some argue that both ripple and dune instabilities result, however, a realistic evaluation of this effect shows that it is much too small to be effective. Naturally occurring bedforms are of finite-amplitude; typically they are asymmetrical, often causing flow separation. This highly non-linear process creates a vastly different flow environment from that assumed in the initial stability case. A wake-like flow structure develops downstream of the separation zone and an internal boundary layer develops beneath. The complex interaction of these two different flow regimes as well as the effect induced by the topography of the bedform itself, produces a shear stress field that dictates the stability of the feature itself.