Explainable deep learning reveals the physical mechanisms behind the turbulent kinetic energy equation

TL;DR

This paper employs explainable deep learning to uncover the physical structures and mechanisms responsible for turbulent kinetic energy transport in channel flow, highlighting hierarchical organization near the wall and its breakdown in the outer layer.

Contribution

The study introduces an explainable deep learning approach using SHAP to identify and analyze turbulence structures, revealing hierarchical organization and dissipation's dominant role.

Findings

Near-wall structures are mainly associated with sweep events.

Hierarchical organization of turbulence exists in the viscous layer.

Classical coherent structures do not fully explain energy budget mechanisms.

Abstract

In this work, we investigate the physical mechanisms governing turbulent kinetic energy transport using explainable deep learning (XDL). An XDL model based on SHapley Additive exPlanations (SHAP) is used to identify and percolate high-importance structures for the evolution of the turbulent kinetic energy budget terms of a turbulent channel flow at a friction Reynolds number of $Re_\tau = 125$. The results show that the important structures are predominantly located in the near-wall region and are more frequently associated with sweep-type events. In the viscous layer, the SHAP structures relevant for production and viscous diffusion are almost entirely contained within those relevant for dissipation, revealing a clear hierarchical organization of near-wall turbulence. In the outer layer, this hierarchical organization breaks down and only velocity-pressure-gradient correlation and turbulent transport SHAP structures remain, with a moderate spatial coincidence of approximately $60\%$. Finally, we show that none of the coherent structures classically studied in turbulence are capable of representing the mechanisms behind the various terms of the turbulent kinetic energy budget throughout the channel. These results reveal dissipation as the dominant organizing mechanism of near-wall turbulence, constraining production and viscous diffusion within a single structural hierarchy that breaks down in the outer layer.