Extracting self-similarity from data
File(s)
Published version
Author(s)
Bempedelis, Nikos
Magri, Luca
Steiros, Konstantinos
Type
Journal Article
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 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.
Date Issued
2025-10-10
Date Acceptance
2025-09-01
Citation
Journal of Fluid Mechanics, 2025, 1020
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1020
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Publication Status
Published
Article Number
A11
Date Publish Online
2025-09-29