Physics of Turbulence

This learning track covers a comprehensive understanding of turbulence physics and hydrodynamics. The track starts with the fundamental concepts such as the incompressible Navier-Stokes equations, vorticity, conservation laws, the continuum approximation and nondimensionalization. The track further provides a comprehensive understanding of of Fourier Space and Fourier Transforms in turbulence and then moves on to the concept of Fourier modes and their correlation to different scales including topics such as flow equations, kinetic energy, vorticity, kinetic helicity, and enstrophy. It also covers the comprehensive understanding of the Craya-Herring Basis in fluid dynamics. Moving on, the track focuses on the different types of instabilities in turbulence such as thermal, rotating convection, magnetoconvection and the role of eigenvalues & eigenvectors along with Lorenz equations and the Rayleigh-Benard convection. The track further introduces the concept of energy transfer in hydrodynamic flows, with a focus on mode to mode transfer, spectral method and Discrete Fourier Transform. It also elaborates on Kolmogorov's theory and Kolmogorov's Four-Fifth law. The track also briefly discusses enstrophy in 3D hydrodynamics and turbulence in 2D flows. Finally, the course covers the concepts of Helical and Scalar Turbulence in fluid dynamics along with a discussion on stably stratified flows, turbulent thermal convection, and flows with vectors before concluding with the intricate subject of Magnetohydrodynamic (MHD) Turbulence.