Capturing multiscale interactions in fluid flow via Lagrangian coherent structures and modal analysis

TL;DR

This paper introduces a data-driven method that links Eulerian modal decompositions with Lagrangian coherent structures in fluid flows, enhancing understanding of multiscale interactions through Lyapunov exponents.

Contribution

It develops a novel framework connecting modal analysis and Lagrangian structures using a sensitivity approach based on finite-time Lyapunov exponents, applicable to various flow regimes.

Findings

Method successfully applied to periodic and turbulent flows.

Provides physical insights into modal-Lagrangian interactions.

Demonstrates applicability to experimental and numerical data.

Abstract

We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of fluid flow in a Lagrangian space. The method, based on the computation of the finite-time Lyapunov exponent, computes the amplitude perturbations experienced by fluid particles due to specific modal components of the flow. Demonstrations of the method are presented for both periodic and turbulent flows, including experimental data from the wake past an oscillating foil, numerical data of the classical cylinder wake flow, and a direct numerical simulation (DNS) of a turbulent channel flow. This method provides a way to understand how Eulerian mode structures interact dynamically with features of the Lagrangian coherent structure across scales, offering additional physical insight into modal decompositions.