Large-eddy simulation has been used to model turbulent channel flow over a range of surfaces featuring a prominent spatial heterogeneity; the flow streamwise direction is aligned relative to the heterogeneity at a range of angles, defined herein with $\unicode[STIX]{x1D703}$ . Prior work has established that a sharp roughness heterogeneity orthogonal to the flow streamwise direction ( $\unicode[STIX]{x1D703}=0$ ) induces formation of an internal boundary layer, which originates at the heterogeneity and thickens in the downflow direction before being homogenized via ambient shear. In contrast, more-recent studies have shown that a sharp roughness heterogeneity parallel to the flow streamwise direction ( $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}/2$ ) induces streamwise-aligned, Reynolds-averaged secondary cells, where the spacing between adjacent surface heterogeneities regulates the spatial extent of secondary cells. No prior study has addressed intermediate (oblique) cases, $0\leqslant \unicode[STIX]{x1D703}\leqslant \unicode[STIX]{x03C0}/2$ . Results presented herein show that the momentum penalty exhibits a nonlinear dependence upon obliquity, where internal boundary layer-like flow processes persist over a range of obliquity angles before abruptly vanishing for spanwise roughness heterogeneity ( $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}/2$ ). This result manifests itself within effective roughness lengths recovered a posteriori : the traditional approach to roughness modelling – predicated upon dependence with surface geometric arguments including height root-mean-square, skewness, frontal- and plan-area index, effective slope. and combinations thereof – is insufficient. A revised model incorporating dependence upon roughness frontal area index and flow-heterogeneity obliquity angle is able to accurately predict effective roughness length a priori .

中文翻译：

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以斜角在异质粗糙度上的湍流通道流动

大涡模拟已被用于对具有显着空间异质性的一系列表面上的湍流通道流动进行建模；流动方向在一定角度范围内相对于异质性对齐，此处定义为 $\unicode[STIX]{x1D703}$ 。先前的工作已经确定，垂直于流动方向的尖锐粗糙度不均匀性（ $\unicode[STIX]{x1D703}=0$ ）诱导内部边界层的形成，该边界层起源于不均匀性并在向下流动方向上变厚，然后通过环境剪切均质化。相比之下，最近的研究表明，平行于流动方向的尖锐粗糙度异质性 ( $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}/2$ ) 导致流向对齐，雷诺 -平均二次细胞，其中相邻表面异质性之间的间距调节次生细胞的空间范围。之前没有研究解决中间（倾斜）情况， $0\leqslant \unicode[STIX]{x1D703}\leqslant \unicode[STIX]{x03C0}/2$ 。此处显示的结果表明，动量惩罚表现出对倾斜度的非线性依赖性，其中内部边界层状流动过程在倾斜角范围内持续存在，然后因展向粗糙度异质性而突然消失（$\unicode[STIX]{x1D703}=\unicode [STIX]{x03C0}/2$）。这个结果在后验恢复的有效粗糙度长度内表现出来：传统的粗糙度建模方法 – 依赖于表面几何参数，包括高度均方根、偏度、正面和平面面积指数、有效坡度。以及它们的组合——是不够的。结合粗糙度锋面指数和流动非均质倾斜角的修正模型能够先验地准确预测有效粗糙度长度。