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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 27 - Spatio-Temporal Instability and Transition (cont.)

Time	Lecture Chapters
[00:07:30]	1. Transient Energy Growth
[00:15:30]	2. Energy-Based Receptivity Analysis

Go to the Course Home or watch other lectures:

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