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Instability and Transition of Fluid Flows

Instability and Transition of Fluid Flows. Instructor: Prof. Tapan K. Sengupta, Department of Aerospace Engineering, IIT Kanpur. This course looks at fluid flow transition - the instabilities that lead the flow to turbulent state. Topics covered in the lectures include: introduction to instability and transition - dynamic stability of still atmosphere, Kelvin-Helmholtz instability; instability and transition in flows - inviscid instability theorems, viscous instability of parallel flows, properties of the Orr-Sommerfeld equation and boundary conditions, instability analysis from the solution of the Orr-Sommerfeld equation, receptivity Analysis of the shear layer, direct simulation of receptivity to free stream excitation; bypass transition; spatio-temporal instability and transition; nonlinear stability - Landau equation and multiple Hopf bifurcation and proper orthogonal decomposition of flow past a cylinder; turbulences - dynamics of turbulence, kinetic energy of fluctuations, Kolmogorov's scaling theory and turbulent length scales. (from nptel.ac.in)

Lecture 08 - Viscous Instability of Parallel Flows (cont.)

Time Lecture Chapters
[00:00:00] 1. Eigenvalue Formulation for Instability of Parallel Flows (cont.)
[00:28:30] 2. Temporal and Spatial Amplification of Disturbances

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Lecture 01 - Introduction to Transition and Turbulence
Lecture 02 - Historical Introduction, Sensitive Dependence of Instability: Effect of Roughness
Lecture 03 - Why We Study Instability? Dynamic Stability of Still Atmosphere
Lecture 04 - Kelvin-Helmholtz Instability
Lecture 05 - Kelvin-Helmholtz Instability (cont.)
Lecture 06 - Parallel Flow Approximation and Inviscid Instability Theorems
Lecture 07 - Inviscid Instability Theorems, Viscous Instability of Parallel Flows
Lecture 08 - Viscous Instability of Parallel Flows (cont.)
Lecture 09 - Properties of the Orr-Sommerfeld Equation and Boundary Conditions
Lecture 10 - Compound Matrix Method (cont.)
Lecture 11 - Instability Analysis from the Solution of the Orr-Sommerfeld Equation
Lecture 12 - Instability Analysis from the Solution of the Orr-Sommerfeld Equation (cont.)
Lecture 13 - Receptivity Analysis of the Shear Layer: Fourier and Laplace Transforms
Lecture 14 - Fourier/Laplace Transforms (cont.)
Lecture 15 - Receptivity to Wall Excitation and Impulse Response
Lecture 16 - Receptivity to Wall Excitation and Impulse Response (cont.), Vibrating Ribbon at the Wall
Lecture 17 - Vibrating Ribbon at the Wall (cont.), General Excitation and Upstream Propagating Modes
Lecture 18 - Low Frequency Free Stream Excitation and the Klebanoff Mode
Lecture 19 - Direct Simulation of Receptivity to Free Stream Excitation
Lecture 20 - Direct Simulation of Receptivity to Free Stream Excitation (cont.)
Lecture 21 - Bypass Transition
Lecture 22 - Bypass Transition (cont.)
Lecture 23 - Bypass Transition (cont.)
Lecture 24 - Bypass Transition (cont.)
Lecture 25 - Instability at the Attachment Line of Swept Wings (cont.)
Lecture 26 - Spatio-Temporal Instability and Transition
Lecture 27 - Spatio-Temporal Instability and Transition (cont.)
Lecture 28 - Spatio-Temporal Instability and Transition (cont.)
Lecture 29 - Nonlinear Stability: Landau Equation and Multiple Hopf Bifurcation
Lecture 30 - Landau Equation and Multiple Hopf Bifurcation
Lecture 31 - Landau Equation and Multiple Hopf Bifurcation (cont.)
Lecture 32 - Proper Orthogonal Decomposition of Flow Past a Cylinder
Lecture 33 - Dynamical System Approach to Flow Instability
Lecture 34 - Turbulence
Lecture 35 - Dynamics of Turbulence
Lecture 36 - Dynamics of Turbulence (cont.), Kinetic Energy of Fluctuations
Lecture 37 - Equilibrium Turbulence and Time Scales in Turbulence (cont.)
Lecture 38 - Spectra, Kolmogorov's Scaling Theory and Turbulent Length Scales (cont.)
Lecture 39 - Kolmogorov's Scaling Theory (cont.), 2D Turbulence