Weakly Nonlinear Stability Analysis for Dune Formation

Abstract

A weakly nonlinear stability analysis of flows over erodible beds is conducted to investigate the formation of dunes. The flow is modeled with the steady vorticity transport equation and the sediment transport is described with Bagnold's bed load–transport rate formula that takes into account the effect of the dune-surface local slope. From the analysis, linear and nonlinear models are derived. Results of the models indicate that although both are able to simulate the instabilities associated with dunes, the nonlinear model predicts more reasonable dune length and development time and is less sensitive to variations of the model parameters. The physical mechanisms controlling the development and downstream migration of dunes also are examined. Predictions of the nonlinear model are in good agreement with selected experimental data.