Numerical computation of sand dune migration with free surface flow

This paper presents a morphodynamic model for free surface flows over bed forms. The model reproduces bed form evolution and migration in a physically based manner. The flow model component of the coupled morphodynamic model, which is two‐dimensional in the streamwise and vertical directions, explicitly treats unsteadiness and nonhydrostatic effects. Comparison with measurements shows that the flow model accurately simulates both mean flow and turbulence structure induced by bed forms under free surface flow. The flow model performance is enhanced by the use of a high‐order Godunov scheme known as the cubic interpolated pseudoparticle (CIP) technique to compute the advection phase of the Navier‐Stokes equation. In addition, an enhanced k‐ɛ turbulence closure with nonlinear terms is incorporated in the present model in order to allow better predictions of Reynolds stress anisotropy in regions with flow separation. Performance of the nonlinear k‐ɛ model is compared with standard k‐ɛ closure in the context of the flow as well as morphodynamic simulation. Nonequilibrium bed load sediment transport is treated using a Eulerian stochastic formulation of the sediment exchange process in terms of pickup and deposition functions. The proposed approach for sediment transport explicitly considers the local flow variability during morphodynamic computation. Model results show that the vertical grid distribution pattern affects the simulation result, particularly for bed form morphodymics. The model successfully simulates some important physical features of bed form evolution, such as amalgamation and asymmetric geometry. The simulation results are in agreement with laboratory experiments as well as some commonly used prediction methods for geometric characteristics of bed forms.