Extracting self-similarity from data

TL;DR

This paper introduces a data-driven method to identify self-similarity variables in complex fluid flows without prior knowledge, using optimization and symbolic regression, validated on classical and turbulent flow problems.

Contribution

It presents a novel approach to extract self-similarity variables directly from data, applicable to complex flows where traditional methods are challenging.

Findings

Successfully recovers known self-similarity expressions in classical problems

Provides new insights into turbulence theories

Demonstrates robustness across numerical and experimental datasets

Abstract

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 optimization problem and symbolic regression. We analyze 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 on single length scale theories of homogeneous turbulence.