Chaos in Turbulence: Understanding Deterministic Behavior

This lecture discusses the relationship between turbulence and deterministic chaos, emphasizing that turbulence is a physical manifestation of chaos. The instructor explains that while deterministic systems are predictable based on initial conditions, chaos introduces sensitivity to these conditions, leading to unpredictable behavior in numerical simulations. The lecture highlights the importance of understanding how uncertainties in measurements can amplify due to chaotic dynamics, making long-term forecasting of turbulent flows challenging. The instructor uses the Lorenz system as an example to illustrate chaotic behavior, showing how trajectories from similar initial conditions can diverge over time. The discussion also contrasts chaotic systems, such as weather patterns in different environments, to characterize their complexity and predictability. The lecture aims to develop quantitative measures of chaos and explore the degrees of freedom involved in chaotic systems, ultimately seeking to understand the intrinsic dynamics of turbulence and chaos.