Large-eddy simulations of unidirectional water flow over dunes

The unidirectional, subcritical flow over fixed dunes is studied numerically using large-eddy simulation, while the immersed boundary method is implemented to incorporate the bed geometry. Results are presented for a typical dune shape and two Reynolds numbers, Re = 17,500 and Re = 93,500, on the basis of bulk velocity and water depth. The numerical predictions of velocity statistics at the low Reynolds number are in very good agreement with available experimental data. A primary recirculation region develops downstream of the dune crest at both Reynolds numbers, while a secondary region develops at the toe of the dune crest only for the low Reynolds number. Downstream of the reattachment point, on the dune stoss, the turbulence intensity in the developing boundary layer is weaker than in comparable equilibrium boundary layers. Coherent vortical structures are identified using the fluctuating pressure field and the second invariant of the velocity gradient tensor. Vorticity is primarily generated at the dune crest in the form of spanwise "roller" structures. Roller structures dominate the flow dynamics near the crest, and are responsible for perturbing the boundary layer downstream of the reattachment point, which leads to the formation of "horseshoe" structures. Horseshoe structures dominate the near-wall dynamics after the reattachment point, do not rise to the free surface, and are distorted by the shear layer of the next crest. The occasional interaction between roller and horseshoe structures generates tube-like "kolk" structures, which rise to the free surface and persist for a long time before attenuating.