Derivation of Kolmogorov's Four-Fifth Law-1 — Lesson 3

This lesson covers the concept of third order tensors, their construction, and their application in physics. It delves into the intricacies of velocities and positions, explaining how they relate to indices and points. The lesson further discusses the construction of second and third order tensors, the concept of delta function, and the asymmetry in tensors. It also introduces the third order correlation function and structure function, explaining how they appear in Kolmogorov's four-fifth law. The lesson concludes with a discussion on the divergence of third order structure function and its connection to spherical symmetry.

Video Highlights

00:13 - Introduction to velocities and positions in the context of tensors
01:30 - Explanation of the delta function and how to construct delta i, j, m
03:22 - Explanation of the incompressible condition
05:26 - Explanation of the concept of Q and its expansion in terms of correlation function
07:06 - Discussion on the concept of homogeneity
15:16 - Discussion on the third order structure function

Key Takeaways

- Third order tensors involve three velocities at two different points.
- The construction of higher order tensors involves the use of delta function and the understanding of asymmetry in tensors.
- The third order correlation function and structure function are key concepts in understanding the behavior of physical systems.
- The divergence of the third order structure function is connected to spherical symmetry.
- The understanding of these concepts is crucial in the application of Kolmogorov's four-fifth law.