Extracting self-similarity from data

Identifying self-similarity is key to understanding and modelling a plethora of phenomena in fluid mechanics. Unfortunately, this is not always possible to perform formally in highly complex flows. We propose a methodology to extract the similarity variables of a self-similar physical process directly from data, without prior knowledge of the governing equations or boundary conditions, based on an optimisation problem and symbolic regression. We analyse the accuracy and robustness of our method in five problems which have been influential in fluid mechanics research: a laminar boundary layer, Burger’s equation, a turbulent wake, a collapsing cavity and decaying turbulence. Our analysis considers datasets acquired via both numerical and wind tunnel experiments. The algorithm recovers the known self-similarity expressions in the first four problems and generates new insights into single length scale theories of homogeneous turbulence.