Formation of Subaqueous Ripples and Dunes: the Solution to an Old Problem?

Abstract:

It is well known from extensive flume and river data the existence of two broad classes of subaqueous bedforms: ripples and dunes, with sizes scaling with grain diameter (ripples) and flow depth (dunes). In spite of recent advances in the understanding of the initial stages of their formation, there is still no physical explanation of the experimental results, and thus no theory predicting both their occurrence and the scaling of the mature bedforms. We address this problem using a well-established aeolian morphodynamic model that was extended to include (i) bedload transport, (ii) Hanratty’s model for dynamically smooth flows and (iii) the hydrodynamic effects of the free surface in dynamically rough flows. Simulations under unidirectional and uniform flow show that steady state ripples form in dynamically smooth conditions and dunes in dynamically transitional ones. Both ripples and dunes result from the nonlinear evolution of an initial flat bed and are clearly distinct from the small-scale bedforms arising during the initial linear stage. In agreement with experimental data, simulated ripples are very regular, scale with the hydrodynamical roughness length and their growth is limited by the internal structure of the flow. In contrast, steady state dunes exhibit a broader range of sizes, their growth is limited by the free surface and thus their maximum size scales with the flow depth.