In search of a universal rough-wall model*

Predicting the drag of the flow past a rough surface is a challenging problem but also of great practical use in engineering and geophysics. There are various types of surface roughness from the Gaussian-spectrum-like random surface to the regular cubical roughness array, and their effects on increasing the drag are highly dependent on the detailed geometry, which makes the prediction of the drag using a single universal model extremely difficult. A critical assessment of the existing models is much helpful to provide a prospective direction for future investigations. In this work, we evaluate the performance of 7 existing rough-wall models based on the flow data of 68 rough surfaces. The seven predicting models include two physics-derived models, three correlation-based models and two data-driven machine learning models. The rough surfaces include both random and regular roughness types which cover a wide range of the roughness parameters (the roughness height, coverage density, skewness, the effective slop etc). The results indicate that the effectiveness of the correlation-based model is limited to a small range of roughness parameters, but the physics-based model provides a much better prediction for a broader range, while the accuracy of the data-driven machine learning models are highly dependent on the data that used to train the neural network.