Enstrophy & Turbulence in Flows

This course covers the complex concepts of enstrophy and turbulence in 3D and 2D flows respectively. It begins with an in-depth exploration of enstrophy in 3D hydrodynamics, including its definition, governing equations, and mode to mode enstrophy transfer. The course emphasizes the role of vorticity and discusses the derivation and significance of enstrophy flux and enstrophy spectrum. It uses the example of how stretching can influence enstrophy to highlight the importance of simulations in understanding this concept. The course then transitions to turbulence in 2D flows, discussing conservation laws, Kraichnan theory, and the formation of structures. It provides real-world applications in astrophysics and atmospheric flows and delves into the conservation laws of energy and enstrophy. The course concludes with a detailed explanation of energy flux and enstrophy flux in steady flows and the application of Kraichnan theory in understanding kinetic energy and enstrophy behavior.