Numerical model of turbulent flow over sand dune

A two-dimensional numerical model, based on solution of the Reynolds-averaged Navier-Stokes equations and the k-omega turbulence model, which takes into account sand-grain roughness, is developed to describe the flow in a fixed dune-bed channel. The model predicts the velocity and turbulence fields, as well as the pressure and friction distributions along the dune. The details of the flow in the separation eddy are calculated. The model predictions are in general agreement with existing detailed experimental data in a rectangular channel with two-dimensional dunes of typical but regular shape. The calculated pressure and friction distributions enable determination of the resistance components of the channel without further empiricism. However, compared to a well-known and representative semiempirical engineering formula for the prediction of resistance of natural dune-bed channels, the two-dimensional numerical model predicts significantly different contributions of friction and pressure to the total resistance, and a much larger total resistance. The numerical model is general enough to be used for channels with different bed topography. Its extension to model the flow in ice-covered channels is in a companion paper.