Kolmogorov's Four-Fifth Law

This course covers the comprehensive understanding of turbulence and Kolmogorov's four-fifth law. It begins with the exploration of 3D hydrodynamic turbulence, focusing on the spectrum and flux in the inertial range. The course explains the role of the Reynolds number in turbulent cascade and the resulting k to minus five-third spectrum. It introduces Pao's model for larger Reynolds numbers and its application in both inertial and dissipation ranges. The course then delves into Kolmogorov's four-fifth law, a fundamental principle in turbulence theory, explaining its derivation process, the assumptions made, and the connection with the five-third law. The course further discusses the concept of third order tensors, their construction, and their application in physics. It concludes with a discussion on the concept of structure functions in turbulence, focusing on second and third order correlation functions.