Revealing Structure and Symmetry of Nonlinearity in Natural and Engineering Flows

TL;DR

This paper introduces Triadic Orthogonal Decomposition (TOD), a novel method for analyzing energy transfer in fluid flows by identifying and quantifying triadic interactions, revealing complex networks of scale interactions in natural and engineering flows.

Contribution

The paper presents TOD, a new technique that captures spectral momentum transfer, characterizes triadic interactions, and uncovers energy exchange laws in turbulent flows.

Findings

TOD identifies coherent flow structures and their energy exchange roles.

Reveals networks of triadic interactions with forward and backward energy transfer.

Applies successfully to wake flow data, demonstrating complex energy transfer mechanisms.

Abstract

Energy transfer across scales is fundamental in fluid dynamics, linking large-scale flow motions to small-scale turbulent structures in engineering and natural environments. Triadic interactions among three wave components form complex networks across scales, challenging understanding and model reduction. We introduce Triadic Orthogonal Decomposition (TOD), a method that identifies coherent flow structures optimally capturing spectral momentum transfer, quantifies their coupling and energy exchange in an energy budget bispectrum, and reveals the regions where they interact. TOD distinguishes three components--a momentum recipient, donor, and catalyst--and recovers laws governing pairwise, six-triad, and global triad conservation. Applied to unsteady cylinder wake and wind turbine wake data, TOD reveals networks of triadic interactions with forward and backward energy transfer across frequencies and scales.