Lagrangian Coherent Structures in Unsteady Fluids with Finite Time Lyapunov Exponents

Explore Lagrangian Coherent Structures (LCS) in unsteady fluids through a comprehensive 46-minute video lecture by Steve Brunton. Delve into the concept of Finite Time Lyapunov Exponents (FTLE) and their role in identifying persistent structures in fluid dynamics. Learn about the importance of LCS as time-varying analogues of stable and unstable manifolds, and how they represent material lines of attraction and repulsion in fluids. Discover the process of computing FTLE fields by analyzing the stretching between neighboring passive particles advected along flow fields. Gain insights into practical applications of LCS in unsteady aerodynamics, jellyfish feeding mechanisms, and ocean mixing. Explore key literature in the field and understand how FTLE can be used as a measure of sensitivity in fluid systems. Perfect for those interested in advanced fluid dynamics, this lecture provides a thorough introduction to LCS and FTLE, complete with real-world examples and theoretical foundations.

Introduction & Overview.
Integrating Particles through Unsteady Flow Fields.
LCS as Stable and Unstable Manifolds.
Literature Review.
Computing FTLE Fields.
FTLE as Material Lines (Separatrices).
LCS for Unsteady Aerodynamics.
LCS Describe How Jellyfish Eat.
FTLE and Mixing.
Mixing in the Ocean.
FTLE as a Measure of Sensitivity.