Flow and coherent structures around circular cylinders in shallow water

Abstract

Eddy-resolving numerical simulations are conducted to investigate the dynamics of the large-scale coherent structures around a circular cylinder in an open channel under very shallow flow conditions where the bed friction significantly affects the wake structure. Results are reported for three test cases, for which the ratio between the cylinder diameter, D, and the channel depth, H, is D/H = 10, 25, and 50, respectively. Simulation results show that a horseshoe vortex system forms in all test cases and the dynamics of the necklace vortices is similar to that during the breakaway sub-regime observed for cases when a laminar horseshoe vortex forms around the base of the cylinder. Given the shallow conditions and turbulence in the incoming channel flow, the necklace vortices occupy a large fraction of the flow depth (they penetrate until the free surface in the shallower cases with D/H = 25 and 50). The oscillations of the necklace vortices become less regular with increasing polar angle magnitude and can induce strong amplification of the bed shear stress beneath their cores. Strong interactions are observed between the legs of the necklace vortices and the eddies shed in the separated shear layers in the cases with D/H = 25 and 50. In these two cases, a vortex-street type wake is formed and strong three-dimensional effects are observed in the near-wake flow. A secondary instability in the form of arrays of co-rotating parallel horizontal vortices develops. Once the roller vortices get away from the cylinder, the horizontal vortices in the array orient themselves along the streamwise direction. This instability is not present for moderately shallow conditions (e.g., D/H ≈ 1) nor for very shallow cases when the wake changes to an unsteady bubble type (e.g., D/H = 50). For cases when this secondary instability is present, the horizontal vortices extend vertically over a large fraction of the flow depth and play an important role in the vertical mixing of fluid situated at the wake edges (e.g., by transporting the near-bed, lower-velocity fluid toward the free surface and vice versa). The largest amplification of the bed shear stress in the near-wake region is observed beneath these horizontal vortices, which means that they would play an important role in promoting bed erosion behind the cylinder in the case of a loose bed. Simulation results suggest that these co-rotating vortices form as a result of the interactions between the legs of the main necklace vortices and the vortical eddies contained into the newly forming roller at the back of the cylinder. The paper also analyzes how D/H affects the separation angle on the cylinder, the size of the recirculation bubble, the bed friction velocity distributions, and turbulence statistics.