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.

对于恒定Froude数下的层流，过渡流和湍流，进行了安装在床上的方棒上的自由表面流的大涡模拟。选择分别对应于过渡粗糙度和k型（重新附着流）粗糙度的两个不同的钢筋间距。用实验数据对湍流模拟进行了验证，并根据水面高度和水流速度剖面获得了令人信服的模拟与测量结果的一致性。水面响应于潜在的床面粗糙度而变形，范围从过渡粗糙度的轻微起伏到k的不同驻波型粗糙度。水面瞬时变形随雷诺数的增加而增加。平均水流速度和壁面法向速度，总剪切应力和水流函数的等值线揭示了两个连续棒之间的槽中存在和扩展了回流区。由于粗糙的床层和变形的水面，流动受到强烈的局部速度梯度的控制。在自由表面上的局部弗洛德数在过渡粗糙度上对于低雷诺数增加，而在k型粗糙度上对于低雷诺数减少。过渡流和湍流的压力系数分布非常相似$C_p$ 在这两种情况下 $C_p$对于层流，通常较低。关于摩擦系数，$C_F$，在湍流情况下明显低于过渡和层流情况。钢筋间距不会显着影响摩擦力和压力对总力的相对贡献，雷诺数也不会。对于过渡粗糙度，摩擦系数更大，并且随着雷诺数的增加而减小。