Turbulence in 2D Flows — Lesson 2

This lesson covers the concept of turbulence in 2D flows, focusing on conservation laws, Kraichnan theory, and the subtleties and fluxes in numerical results. It explores the real-world applications of 2D flows, such as in astrophysics and atmospheric flows, and discusses the formation of structures in 2D flows. The lesson also delves into the conservation laws of energy and enstrophy, and the role of vorticity in 2D flows. It further explains the concept of fluxes, particularly energy flux and enstrophy flux, and their implications in steady flows. The lesson concludes with a discussion on Kraichnan theory and its application in understanding the behavior of kinetic energy and enstrophy in 2D flows.

Video Highlights

00:21 - Explanation of conservation laws and Kraichnan theory
02:32 - Discussion on the conservation of kinetic energy and enstrophy in 2D flows
10:56 - Explanation of the concept of inverse cascade of energy and computation of fluxes in 2D flows
23:01 - Explanation of the Pao's model and its application in 2D flows
39:31 - Discussion on the simulation results and their comparison with theoretical predictions

Key Takeaways

- Conservation laws play a crucial role in understanding 2D flows.
- In 2D flows, both energy and enstrophy are conserved.
- Vorticity in 2D flows does not increase or decrease, but is advected.
- Fluxes, particularly energy flux and enstrophy flux, are important in understanding the behavior of 2D flows.
- Kraichnan theory provides insights into the behavior of kinetic energy and enstrophy in 2D flows.