The downward shift of the mean velocity profile in the logarithmic region, known as roughness function , $$\Delta U^+$$ Δ U + , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re $$_{\tau }$$ τ . In the present work, the effects of several geometrical parameters on the roughness function, in both transitional and fully rough regimes, are investigated by means of large eddy simulation of channel flows characterized by different wall-roughness textures at different values of Re $$_{\tau }$$ τ up to 1000. The roughness geometry is generated by the superimposition of sinusoidal functions with random amplitudes and it is exactly resolved in the simulations. A total number of 10 cases are solved. With the aim to find a universal correlation between the roughness geometry and the induced roughness function, we analyzed the effect of more than a single geometrical parameter, including the effective slope, which takes into account both the roughness height and its texture. Based on data obtained from our simulations and a number of data points from the literature, a correlation between the ES and the root mean square of the roughness oscillation, as well as between ES and the mean absolute deviation of the roughness, satisfactorily predicts the roughness function.

中文翻译：

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以不规则粗糙度为边界的粗糙湍流通道流的大涡模拟：向通用粗糙度相关性发展

对数区域平均速度剖面的向下移动，称为粗糙度函数，$$\Delta U^+$$ Δ U + ，是壁面有界流动中粗糙度的主要宏观效应。这种速度下降与摩擦雷诺数和定义粗糙度模式的几何特性（如粗糙度高度、密度、形状参数）严格相关，在过去的几十年中已经得到深入研究。在几何参数中，有效斜率 (ES) 似乎适合估计固定摩擦雷诺数 Re $$_{\tau }$$ τ 下的粗糙度函数。在目前的工作中，几个几何参数对粗糙度函数的影响，在过渡和完全粗糙的状态下，通过对通道流的大涡模拟进行研究，该通道流的特征在于不同的壁粗糙度纹理，在不同的 Re $$_{\tau }$$ τ 值高达 1000。粗糙度几何是通过叠加随机正弦函数生成的振幅，它在模拟中得到了精确解决。一共解决了10个案例。为了找到粗糙度几何形状和诱导粗糙度函数之间的普遍相关性，我们分析了多个几何参数的影响，包括有效坡度，它同时考虑了粗糙度高度及其纹理。基于从我们的模拟中获得的数据和文献中的一些数据点，ES 与粗糙度振荡的均方根之间的相关性，