Rough-wall modeling on a low-dimensional manifold

Predicting drag caused by turbulent flow over rough surfaces remains one of the most challenging problems in engineering due to the intricate interactions between turbulent flow and surface roughness. This complexity is further heightened by the wide variability in rough-wall topographies and the roughness statistics required to accurately represent rough surfaces. In this study, we propose an approach to rough-wall modeling for drag prediction using deep convolutional autoencoders. We first compress complex data of 93 distinct rough surfaces into a low-dimensional space of just three variables using an autoencoder. These rough-wall topographies are obtained from various experiments and direct numerical simulation studies. We then utilize this reduced-order representation and relate these to the equivalent sandgrain roughness height (ks) with the help of a feedforward neural network. The predictive accuracy of the resulting rough-wall model is further assessed against unseen rough surfaces generated from reconstructions obtained from the latent space in unexplored areas. We observe that the formulated rough-wall model predicts ks values for these previously unseen surfaces to a reasonable accuracy. The present findings suggest the potential for ultra-low-dimensional data-driven representations of complex surface roughness and demonstrate their relevance in constructing generalizable predictive models for rough-wall bounded turbulence.