Calculation of dune morphology

Abstract

[1] The shape and dimensions of dunes formed in an erodible bed and exposed to flowing water are investigated by using a numerical model. The flow is calculated using a curvilinear flow model, where we combine a k-ε turbulence closure scheme with a sediment-transport description and the equation of continuity for the sand bed. The complete flow description allows for a discussion about what determines the length of dunes: From the equation of continuity for sediment, it turns out that the sediment transport over dunes is proportional to the local height of the dune. This means that the maximum height of the sand wave occurs at the location of maximum sediment transport. We relate the dune length to the location of maximum sediment transport. It is demonstrated that the effect of streamline curvature is essential for determining the location of maximum sediment transport at low bed shear stresses, due to an overshoot in bed shear stress. For large dimensionless bed shear stresses the downstream decay of turbulence from the former dune is demonstrated to play a major role. Copyright 2005 by the American Geophysical Union.