Direct numerical simulations of fully-developed turbulent channel flow with irregular rough walls have been performed at four friction Reynolds numbers, namely, 180, 240, 360 and 540, yielding data in both the transitionally- and fully-rough regime. The same roughness topography, which was synthesised with an irregular, isotropic and near-Gaussian height distribution, is used in each simulation. Particular attention is directed towards the wall-normal variation of flow statistics in the near-roughness region and the fluid-occupied region beneath the crests, i.e. within the roughness canopy itself. The goal of this study is twofold. (i) Provide a detailed account of first- and second-order double-averaged velocity statistics (including profiles of mean velocity, dispersive stresses, Reynolds stresses, shear stress gradients and an analysis of the mean force balance) with the overall aim of understanding the relative importance of “form-induced” and “turbulence-induced” quantities as a function of the friction Reynolds number. (ii) Investigate the possibility of predicting the levels of streamwise dispersive stress using a phenomenological closure model. Such an approach has been applied successfully in the context of idealised vegetation canopies (Moltchanov & Shavit, 2013, Water Resour. Res., vol. 49, pp. 8222-8233) and is extended here, for the first time, to an irregular rough surface. Overall, the results reveal that strong levels of dispersive stress occur beneath the roughness crests and, for the highest friction Reynolds number considered in this study, show that the magnitude (and gradient) of these “form-induced” stresses exceed their Reynolds stress counterparts. In addition, this study emphasises that the dominant source of spatial heterogeneity within the irregular roughness canopy are “wake-occupied” regions and that a suitable parameterisation of the wake-occupied area is required to obtain an accurate prediction of streamwise dispersive stress.

中文翻译：

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在经过不规则的近高斯粗糙度的湍流通道流中雷诺和分散应力的雷诺数依赖性

在四个摩擦雷诺数下，即 180、240、360 和 540，对具有不规则粗糙壁的完全发展的湍流通道流动进行了直接数值模拟，产生了过渡和完全粗糙状态的数据。在每个模拟中都使用相同的粗糙度地形，它是用不规则的、各向同性的和接近高斯的高度分布合成的。特别注意近粗糙度区域和波峰下方的流体占据区域（即粗糙度冠层本身）中流动统计的壁面法向变化。这项研究的目标是双重的。(i) 提供一阶和二阶双平均速度统计的详细说明（包括平均速度、分散应力、雷诺应力、剪应力梯度和平均力平衡分析），总体目标是了解“形状诱导”和“湍流诱导”量作为摩擦雷诺数的函数的相对重要性。(ii) 研究使用现象学闭合模型预测流向色散应力水平的可能性。这种方法已成功应用于理想化植被冠层 (Moltchanov & Shavit, 2013, Water Resour. Res., vol. 49, pp. 8222-8233) 并在此处首次扩展到不规则的粗糙的表面。总体而言，结果表明，在粗糙波峰下方出现了很强的分散应力，对于本研究中考虑的最高摩擦雷诺数，表明这些“形状诱导”应力的大小（和梯度）超过了它们的雷诺应力对应物。此外，本研究强调，不规则粗糙度冠层内空间异质性的主要来源是“尾流占据”区域，需要对尾流占据区域进行适当的参数化，以获得对流向分散应力的准确预测。