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Physics of Turbulence

Physics of Turbulence. Instructor: Prof. Mahendra k. Verma, Department of Physics, IIT Kanpur. Turbulence is everywhere in the interiors and atmospheres of planets and stars, galaxies, biological systems including human body, engineering flows, etc. In this course, we will cover fundamental aspects of turbulence: Kolmogorov's theory of turbulence in spectral and real space; Two-dimensional turbulence; Energy transfers; Enstrophy and kinetic helicity cascades; more complex applications, such as passive scalar, Turbulent thermal convection, and Magnetohydrodynamic turbulence. (from nptel.ac.in)

Lecture 09 - Fourier Space Representation: Vorticity, Kinetic Helicity, and Enstrophy


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Lecture 01 - The Turbulence Problem
Lecture 02 - Basic Hydrodynamics: Governing Equations
Lecture 03 - Basic Hydrodynamics: Vorticity
Lecture 04 - Basic Hydrodynamics: Conservation Laws
Lecture 05 - Basic Hydrodynamics: Example Problems
Lecture 06 - Fourier Space Representation: Definitions
Lecture 07 - Fourier Space Representation: Flow Equations
Lecture 08 - Fourier Space Representation: Kinetic Energy
Lecture 09 - Fourier Space Representation: Vorticity, Kinetic Helicity, and Enstrophy
Lecture 10 - Fourier Space Representation: Examples
Lecture 11 - Fourier Space Representation: Examples (cont.)
Lecture 12 - Craya-Herring Basis: Definitions
Lecture 13 - Craya-Herring Basis: Equations of Motion for a Triad
Lecture 14 - Craya-Herring Basis: Equations of Motion for an Anticlockwise Triad
Lecture 15 - Thermal Instability
Lecture 16 - Thermal Instabilities (cont.)
Lecture 17 - Rotating Convection: Instability and Patterns
Lecture 18 - Magnetoconvection: Instability and Patterns
Lecture 19 - Nonlinear Saturation: Lorenz Equation
Lecture 20 - Patterns, Chaos, and Turbulence
Lecture 21 - Energy Transfers: Mode-to-Mode Energy Transfers
Lecture 22 - Energy Transfers: Mode-to-Mode Energy Transfers (cont.)
Lecture 23 - Energy Transfers: Examples
Lecture 24 - Energy Transfers: Spectral Energy Flux and Shell-to-Shell Energy Transfer
Lecture 25 - Energy Transfers: Fluid Simulations using Spectral Method
Lecture 26 - Energy Transfers: Fluid Simulations - Dealiasing
Lecture 27 - Kolmogorov's Theory: Energy Spectrum and Flux
Lecture 28 - Kolmogorov's Theory: Insights and its Verification with Direct Numerical Simulation
Lecture 29 - Kolmogorov's Theory: Spectrum and Flux in Inertial-dissipation Range
Lecture 30 - Kolmogorov's Four-Fifth Law: Isotropic Tensor and Correlations
Lecture 31 - Kolmogorov's Four-Fifth Law: Derivation
Lecture 32 - Kolmogorov's Four-Fifth Law: Derivation (Final Steps)
Lecture 33 - Energy Spectrum and Flux
Lecture 34 - Two-dimensional Turbulence
Lecture 35 - Helical Turbulence
Lecture 36 - Flow with a Scalar
Lecture 37 - Passive Scalar Turbulence
Lecture 38 - Stably Stratified Turbulence
Lecture 39 - Turbulent Thermal Convection
Lecture 40 - Flow with a Vector
Lecture 41 - MHD (MagnetoHydroDynamic) Turbulence: Formalism
Lecture 42 - MHD Turbulence: Energy Transfers
Lecture 43 - MHD Turbulence: Turbulence Models
Lecture 44 - MHD Turbulence: Dynamo