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.
Physics of Turbulence
Innovation Course
Turbulence & Hydrodynamics
This course covers the intricate subjects of turbulence physics and hydrodynamics. It starts with a simple example of a room heater to illustrate the concept of heat diffusion and its relation to turbulence. The course delves into the diffusion equation, turbulence's si...Read more
Innovation Course
Fourier Space Representation & Transformations
This course covers the intricate subjects of turbulence physics and hydrodynamics. It starts with a simple example of a room heater to illustrate the concept of heat diffusion and its relation to turbulence. The course delves into the diffusion equat...Read more
Innovation Course
Craya-Herring Basis in Fluid Dynamics
This course covers the comprehensive understanding of the Craya-Herring Basis in fluid dynamics. It starts with the basic concept of Craya-Herring Basis, its advantages, and the construction of equations in 2D and 3D. The course further delves into the conc...Read more
Innovation Course
Instabilities in Turbulence - I
This course covers the intricate concepts of turbulence in fluids, instability in fluid systems, and the application of eigenvalues and eigenvectors in linear equations. For instance, the course delves into the occurrence of turbulence in different systems such as ...Read more
Innovation Course
Instabilities in Turbulence - II
This course covers the intricate concepts of instabilities in various systems, with a special focus on magnetoconvection and turbulence. It begins with an exploration of how a fluid contained between two plates can generate local magnetic fields when a mean magnet...Read more
Innovation Course
Energy Transfers in Hydrodynamics
This course covers the comprehensive understanding of energy transfers in hydrodynamic flows, with a focus on turbulence and the Navier-Stokes equation. It delves into the concept of mode to mode energy transfer, explaining how energy moves from one region to a...Read more
Innovation Course
Kolmogorov's Theory & Turbulence
This course covers the fundamental concepts of turbulence in fluid dynamics, focusing on the Kolmogorov's theory. It provides an in-depth understanding of how to simulate hydrodynamic flow and compute energy transfer. The course further elaborates on the computatio...Read more
Innovation Course
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...Read more
Innovation Course
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 cou...Read more
Innovation Course
Helical & Scalar Turbulence
This course covers the intricate concepts of Helical and Scalar Turbulence in fluid dynamics. It begins with an exploration of kinetic helicity, its control, and its relation to viscosity. For instance, the course delves into the conservation laws, kinetic helicity tra...Read more
Innovation Course
Stratified Flows & Convection
This course covers the intricate concepts of stably stratified flows, turbulent thermal convection, and flows with vectors. For instance, it begins with the configuration of stably stratified turbulence, where the dense fluid sits at the bottom due to gravity and the...Read more
Innovation Course
Magnetohydrodynamic Turbulence
This course covers the intricate subject of Magnetohydrodynamic (MHD) Turbulence, providing a comprehensive understanding of the interaction between velocity and magnetic fields, akin to how a river's current affects a floating log's movement. The course delves in...Read more
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