Ripple and dune formation in rivers

A linear stability analysis for dune and ripple formation is presented that implements a rotational two-dimensional flow model valid in the smooth as well as in the transitional and rough flow regimes. Sediment is assumed to be transported as bedload, disregarding the role of suspension. Therefore, the main mechanism driving instability, for both ripples and dunes, is the phase lag between bed shear stress and bed elevation. Ripples are shown to be confined to relatively low values of the Shields parameter and of the particle Reynolds number. For higher values of the Shields parameter and of the particle Reynolds number (and thus of the Froude number and of the roughness Reynolds number), ripples are replaced by dunes. The present analysis ultimately allows for a successful unification of the theories of dune and ripple formation and for a clarification of the debated role of ripples on the formation of dunes. A good agreement between predicted and observed wavelengths for both ripples and dunes is found.