Free surface flow over square bars at different Reynolds numbers

Large-eddy simulations of free surface flow over bed-mounted square bars are performed for laminar, transitional and turbulent flows at constant Froude number. Two different bar spacings are selected corresponding to transitional and k-type (reattaching flow) roughness, respectively. The turbulent flow simulations are validated with experimental data and convincing agreement between simulation and measurement is obtained in terms of water surface elevations and streamwise velocity profiles. The water surface deforms in response to the underlying bed roughness ranging from mild undulation for transitional roughness to distinct standing waves for k-type roughness. The instantaneous water surface deformations increase with an increase in Reynolds number. Contours of the mean streamwise and wall-normal velocities, the total shear stress and the streamfunction reveal the presence and extension of recirculation zones in the trough between two consecutive bars. The flow is governed by strong local velocity gradients as a result of the rough bed and the deformed water surface. The local Froude number at the free surface increases for low Reynolds number in the flow over transitional roughness and decreases for low Reynolds number in the flow over k-type roughness. The transitional and turbulent flows exhibit a very similar distribution of the pressure coefficient C_p in both cases, whilst C_p is generally lower for the laminar flow. Regarding the friction coefficient, C_f, it is significantly lower in the turbulent case than in the transitional and laminar cases. The bar spacing does not affect significantly the relative contribution of friction and pressure forces to the total force, neither does the Reynolds number. The friction factor is greater for transitional roughness and decreases with increasing Reynolds number.