Introduction to Kolmogorov's Four-Fifth Law — Lesson 2

This lesson covers the concept of Kolmogorov's four-fifth law, a fundamental principle in turbulence theory. The lesson delves into the real space description of the law, which was derived in 1941 by Kolmogorov. The lesson explains the derivation process, the assumptions made, and the connection with the five-third law. It also discusses the concept of homogeneity and isotropy, and how these properties are applied in the context of the law. The lesson further explores the correlation function, the Taylor micro scale, and the Reynolds number based on the Taylor micro scale. For instance, if we consider a turbulent flow started with similar initial conditions, the average over many copies is called the ensemble average.

Video Highlights

00:14 - Introduction to Kolmogorov's four-fifth law and its derivation in real space
04:40 - Explanation of isotropic tensor and its application in deriving the Kolmogorov structure function
10:25 - Discussion on the properties of isotropic vectors and tensors
19:18 - Discussion on the second order correlation function in turbulence
39:35 - Explanation of the concept of Taylor micro scale and its relation to Reynolds number

Key Takeaways

- Kolmogorov's four-fifth law is a fundamental principle in turbulence theory, derived in 1941.
- The law is derived under certain assumptions like viscosity going to 0 limit steady state.
- Homogeneity and isotropy are key properties applied in the context of the law.
- The correlation function, the Taylor micro scale, and the Reynolds number based on the Taylor micro scale are important concepts in understanding the law.
- The ensemble average is obtained by taking many copies of turbulent flow started with similar initial conditions.