This paper studies the 3-D turbulent channel flows over rough walls with stochastic roughness height distributions by using the large eddy simulation and the immersed boundary method. The obtained mean and fluctuating velocity profiles for the smooth and rough channel flows agree well with the available numerical and experimental results. The stochastic surface roughness is found to have a more significant influence than the uniform surface roughness on the turbulent velocity statistics and the coherent structures, with the same average roughness height. With a greater variation in the roughness height, the mean velocity and the streamwise fluctuating velocity is decreased and the spanwise velocity and the wall-normal fluctuating velocity are increased. In addition, one observes larger and more profuse quasi-streamwise vortices, hairpin vortices and elongated structures above the crest plane of the roughness array in cases of highly stochastic rough walls. However, the low-speed streaky structures are broken up locally and the ejection and sweep events are depressed by the stochastic roughness below the average roughness height. The results of this study support Townsend’s wall-similarity hypothesis for both stochastic and uniform rough wall turbulences, demonstrating that in both cases the effects of the surface roughness on the turbulent flow are limited to the rough sub-layer.

中文翻译：

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具有随机粗糙度高度分布的粗糙壁上湍流通道流动的大涡模拟

本文利用大涡模拟和沉浸边界方法研究了粗糙高度随机分布在粗糙壁上的三维湍流通道。所获得的平滑和粗糙通道流动的平均速度曲线和波动速度曲线与可用的数值和实验结果非常吻合。在相同的平均粗糙度高度下，发现随机表面粗糙度比均匀表面粗糙度对湍流速度统计数据和相干结构的影响更大。随着粗糙度高度的变化，平均速度和流向波动速度减小，而翼展方向速度和壁法向波动速度增大。此外，人们观察到更大且更丰富的准流涡旋，在高度随机的粗糙壁的情况下，在粗糙阵列的波峰平面上方的发夹涡旋和细长结构。然而，低速条纹结构在局部被破坏，并且喷射和扫掠事件被低于平均粗糙度高度的随机粗糙度所抑制。这项研究的结果支持了汤森德关于随机和均匀粗糙壁湍流的壁相似性假说，表明在两种情况下，表面粗糙度对湍流的影响都限于粗糙子层。