The role of the areal parameters on turbulent flow over 2D Gaussian roughness

In the past decades, numerous efforts have been dedicated to establishing a direct correlation between a geometric parameter that represents wall roughness and the corresponding velocity reduction, known as the Roughness Function ΔU+. This reduction is influenced by various statistical measures of roughness height, including average roughness height, peak-to-valley roughness distance, roughness root mean square, and Effective Slope, among others. It has been demonstrated that a singular measure of roughness height cannot sufficiently predict the Roughness Function across all turbulent regimes. Consequently, many studies have concentrated on identifying a universal correlation between roughness geometry and the downward shift of the mean velocity profile. In this study, we investigated the correlation between various geometrical parameters and the Roughness Function using Large Eddy Simulation (LES) techniques in channel flows at a friction Reynolds number of Reτ=400. Given the complexity introduced by the random nature of irregular roughness, we explored specific aspects of the relationship between wall irregularities and the roughness function by studying 2D geometries. This approach allowed us to systematically investigate the impact of geometrical properties on the roughness function and isolate the effects of roughness density and coverage area. Several irregular rough surfaces, characterized by different average oscillations height, different distributions and different densities, were designed throughout 2D Gaussian functions. With the aim to find a universal correlation between the roughness geometry and the Roughness Function, new geometrical quantities were investigated, based on the global area occupied by the roughness A∗. The prediction of the roughness function can be thus obtained using apriori data. To predict the roughness function, we introduced a parameter called Effective Area (EA), which is derived from the correlation between the Effective Slope (ES) and the roughness area A∗. Our findings indicate that a single geometric parameter, whether ES or Area A, is insufficient to predict the roughness effect. Conversely, combining these two parameters enhances predictive accuracy, at least for the proposed roughness model. This improvement can be attributed to the ability of ES to interpret the roughness distribution and height, while the coverage area is effective in predicting roughness density over a flat plate.