Capturing Turbulent Dynamics and Statistics in Experiments Using Exact Coherent States

Explore the dynamics and statistics of turbulent flows in this seminar by Balachandra Suri from the Institute of Science and Technology, Austria. Delve into the concept of Exact Coherent States (ECS) as a framework for predicting turbulent behavior. Learn how coherent structures in moderately turbulent quasi-two-dimensional laboratory flows relate to ECS. Discover a low-dimensional model for forecasting turbulent evolution and understand how frequently appearing ECS capture statistical averages of turbulent flows. Gain insights into the geometrical description of transient turbulence using dynamical connections between ECS. Examine topics such as spatially extended nonlinear systems, Kolmogorov flow, unstable equilibria, and unstable periodic orbits in both numerical simulations and experiments. Investigate the statistical significance of ECS in predicting averages and explore the connectivity between ECS through heteroclinic and homoclinic connections. Conclude with a network model of turbulence that provides a new perspective on this complex phenomenon.

Intro
Research Interests (Numerics and Experiments)
Spatially Extended Nonlinear Systems
Linear vs. Nonlinear Systems
Low-Dimensional Chaos
Order in Chaos
Outline of the Talk
Fluid Flows
Laminar and Turbulent Flows
Order in Turbulence
Exact Coherent States (ECS)
Previous Studies
Kolmogorov Flow
Theoretical Modeling
Turbulent Dynamics
Signatures of Unstable Equilibria
Equilibria from Experiment
The Linear Dynamical Model
Forecasting Turbulence
Expanding Eigendirections
Unstable Periodic Orbits (DNS)
UPOs in Experiment
Statistical Significance of UPOS
Predicting Statistical Averages
Connectivity Between ECS
Heteroclinic Connections (1)
A Homoclinic Connection
Network Model of Turbulence
Summary