The influence of surface anisotropy upon the near-wall region of a rough-wall turbulent channel flow is investigated using direct numerical simulation (DNS). A set of nine irregular rough surfaces with fixed mean peak-to-valley height, near-Gaussian height distributions and specified streamwise and spanwise correlation lengths were synthesised using a surface generation algorithm. By defining the surface anisotropy ratio (SAR) as the ratio of the streamwise and spanwise correlation lengths of the surface, we demonstrate that surfaces with a strong spanwise anisotropy (SAR < 1) can induce an over 200 % increase in the roughness function Δ U + , compared to their streamwise anisotropic (SAR > 1) equivalent. Furthermore, we find that the relationship between the roughness function Δ U + and the SAR parameter approximately follows an exponentially decaying function. The statistical response of the near-wall flow is studied using a “double-averaging” methodology in order to distinguish form-induced “dispersive” stresses from their turbulent counterparts. Outer-layer similarity is recovered for the mean velocity defect profile as well as the Reynolds stresses. The dispersive stresses all attain their maxima within the roughness canopy. Only the streamwise dispersive stress reaches levels that are comparable to the equivalent Reynolds stress, with surfaces of high SAR attaining the highest levels of streamwise dispersive stress. The Reynolds stress anisotropy also shows distinct differences between cases with strong streamwise anisotropy that stay close to an axisymmetric, rod-like state for all wall-normal locations, compared to cases with spanwise anisotropy where an axisymmetric, disk-like state of the Reynolds stress anisotropy tensor is observed around the roughness mean plane. Overall, the results from this study underline that the drag penalty incurred by a rough surface is strongly influenced by the surface topography and highlight its impact upon the mean momentum deficit in the outer flow as well as the Reynolds and dispersive stresses within the roughness layer.

中文翻译：

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表面各向异性对不规则粗糙度湍流的影响

使用直接数值模拟 (DNS) 研究表面各向异性对粗糙壁湍流通道流的近壁区域的影响。使用表面生成算法合成了一组九个具有固定平均峰谷高度、近高斯高度分布和指定的流向和展向相关长度的不规则粗糙表面。通过将表面各向异性比 (SAR) 定义为表面的流向和展向相关长度之比，我们证明了具有强展向各向异性 (SAR < 1) 的表面可以导致粗糙度函数 Δ U 增加 200% 以上+ ，与它们的流向各向异性 (SAR > 1) 等效值相比。此外，我们发现粗糙度函数 Δ U + 和 SAR 参数之间的关系近似遵循指数衰减函数。使用“双平均”方法研究近壁流的统计响应，以区分形式引起的“分散”应力与其湍流对应物。恢复平均速度缺陷剖面以及雷诺应力的外层相似性。分散应力都在粗糙度冠层内达到最大值。只有流向色散应力达到与等效雷诺应力相当的水平，高 SAR 表面达到流向色散应力的最高水平。雷诺应力各向异性还显示出在具有强流向各向异性的情况之间存在明显差异，这些情况在所有壁法线位置都接近轴对称、棒状状态，而具有展向各向异性的情况（雷诺应力的轴对称、盘状状态）在粗糙度平均平面周围观察到各向异性张量。总的来说，这项研究的结果强调了粗糙表面引起的阻力损失受表面形貌的强烈影响，并突出了它对外部流动中的平均动量赤字以及粗糙层内的雷诺和分散应力的影响。在粗糙度平均平面周围观察到雷诺应力各向异性张量的盘状状态。总的来说，这项研究的结果强调了粗糙表面引起的阻力损失受表面形貌的强烈影响，并突出了它对外部流动中的平均动量赤字以及粗糙层内的雷诺和分散应力的影响。在粗糙度平均平面周围观察到雷诺应力各向异性张量的盘状状态。总的来说，这项研究的结果强调了粗糙表面引起的阻力损失受表面形貌的强烈影响，并突出了它对外部流动中的平均动量赤字以及粗糙层内的雷诺和分散应力的影响。