Discovery of knowledge of wall-bounded turbulence via symbolic regression

TL;DR

This paper employs symbolic regression to derive a physically interpretable, general mixing length formula for wall-bounded turbulence, validated across multiple cases, demonstrating the potential of 'white box' machine learning in turbulence research.

Contribution

The paper introduces a novel symbolic regression approach to discover a universal, physically interpretable mixing length formula for wall-bounded turbulence, validated through RANS simulations.

Findings

The derived formula accurately predicts turbulence behavior in various regions.

The formula exhibits correct asymptotic relationships in different turbulence layers.

Symbolic regression effectively uncovers general laws from complex turbulent data.

Abstract

With the development of high performance computer and experimental technology, the study of turbulence has accumulated a large number of high fidelity data. However, few general turbulence knowledge has been found from the data. So we use the symbolic regression (SR) method to find a new mixing length formula which is generally valid in wall-bounded turbulence, and this formula has physical interpretation that it has correct asymptotic relationships in viscous sublayer,buffer layer, log-law region and outer region. Coupled with Reynolds averaged Navier-Stokes (RANS) solver, we test several classic cases. The prediction results fully demonstrate the accuracy and generalization of the formula. So far, we have found that SR method can help us find general laws from complex turbulent systems, and it is expected that through this 'white box' machine learning method, more turbulence knowledge with physical interpretation can be found in the future.