Rough-wall modelling on a low-dimensional manifold*

Linking rough surface topography to the drag experienced by turbulent flow over it is a challenging problem, owing to the wide range of roughness possible. Conventional roughness parameters, which involve roughness height statistics, may be suboptimal in their ability to construct rough-wall models. A novel approach to rough-wall modelling using deep convolutional autoencoders is being proposed for drag prediction. A low-dimensional encoding of 3 latent space variables was derived from a dataset comprising 100 rough wall height distributions. These rough surfaces were obtained from rough walls used in various experiments and Direct Numerical Simulation (DNS) studies. A Feedforward Neural Network (FNN) was trained on these learned representations and the associated equivalent sand-grain roughness height (k_s) values in developing a rough-wall model. Further, new surfaces are constructed by the decoder in latent space regions not occupied by the training dataset. We observe that the formulated FNN rough-wall model predicts k_s values for these previously unseen surfaces to a reasonable accuracy. The present findings suggest that these newly discovered roughness parameters could not only pave the way for rough-wall modelling but also offer an interpolative basis that could cover a wide range of rough surfaces.