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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 34 - Two-dimensional Turbulence

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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