Modal analysis with Lagrangian coherent structures*

Advances in modal analysis methods over the past decade have provided significant insights into dynamically impact coherent features in fluid flow, albeit primarily from an Eulerian perspective. We present a new approach for analyzing the effects of modal perturbations on Lagrangian Coherent Structures (LCSs). Specifically, we consider how modes obtained from methods such as proper orthogonal decomposition and dynamic mode decomposition impact LCSs. Using the model sensitivity framework developed by Kaszás and Haller (2020), we define "mode sensitivity" as the impact of particular mode perturbations on the flow structure, i.e., whereby the perturbations may present as organized patterns rather than random noise. We demonstrate the method on turbulent and periodic flows, including a kinematic flow model, experimental data from an oscillating foil wake, and a turbulent channel flow from the Johns Hopkins Turbulence Database. The results suggests that that the mode sensitivity fields reveal both quantitatively and qualitatively how the finite-time Lyapunov exponent fields from a primary dynamical system change when adding or removing certain modes or external perturbations.