Three-Dimensional and Depth-Averaged Large-Eddy Simulations of Some Shallow Water Flows

Three-dimensional (3D) and two-dimensional (2D) depth-averaged (DA) large-eddy simulations (LES) are presented for three different shallow-water flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder, and the flow in a groyne field. The results are compared with each other and also with experiments. In the 3D-LES, most of the energy-containing turbulent motions, including the larger subdepth-scale motions, are resolved, while in the 2D-DA-LES the effect of the 3D subdepth-scale turbulence is represented by a quadratic bottom-friction model and a simple eddy-viscosity model. In the case of the mixing layer, an additional stochastic backscatter model is necessary to account for the energy transfer from the subdepth-scale turbulence to the 2D structures in order to generate the latter. The 3D-LES results are generally in good agreement with the experiments, including the evolution of the horizontal structures. The much more economic 2D-DA-LES are somewhat less realistic in detail but also produce results that are generally of sufficient accuracy for practical purposes.