Unit 1

Onset of Turbulence: Laminar Flow, Transition, Turbulent Flow – Laminar-Turbulent Transition: Taylor’s Rotating Cylinder Experiment, Benard’s Natural Convection Experiment, Reynolds Experiment, Reynolds Number Concept Based on Volume Flux and Pressure Gradient – Stability Theory of Laminar Flows: Method of Small Disturbances, Orr-Sommerfeld Equation, Modes of Stability, Curve of Neutral Stability, Indifference Reynolds Number, Absolute and Convective Instabilities.

Unit 2

Inviscid Instability: Rayleigh Equation, Point of Inflection Criteria, Critical Layer – Fundamentals of Turbulent Flow: Mean Motion, Fluctuations, Quasi-steady Approach, Apparent Viscosity, Reynolds Stresses (Momentum Theorem & Navier-Stokes Equations), Classical Empirical Results on Turbulence, Wind-tunnel Turbulence.

Unit 3

Semi-empirical Hypothesis: Eddy Viscosity, Prandtl Mixing Length – Isotropic Turbulence: Kolmogorov Hypothesis, Kolmogorov Length and Time Scales – Free Turbulent Flows: Jet Boundary, Free Jet, Wake.

Course Objectives

The purpose of this subject is to familiarize instability analysis and its application in the theoretical characterization of laminar-turbulent transition. In addition, it will also help students to appreciate and understand the relevance of credible hypothesis crucial for turbulence models. Thereby, students will acquire and be capable to utilize this fundamental understanding for many practically relevant turbulent flows

Course Outcomes

• CO1: Develop theoretical characterization for laminar-turbulent flow transition.
• CO2: Examine the nature of turbulence based on classical theory and empirical results.
• CO3: Comprehend closure problem pertinent to turbulence and make use of turbulence models to study the nature of turbulence.
• CO4: Apply standard hypothesis to quantify eddy structures and implement the basic concepts to refine existing turbulence models.
• CO5: Distinguish the delicate aspects of turbulent boundary layer flows from free turbulent flows

CO – PO Mapping

Textbook(s)

• Herrmann Schlichting, Klaus Gersten, “Boundary Layer Theory,” 8^th edition, Springer-Verlag, 2000.

Reference(s)

• Pijush K. Kundu, Ira M. Cohen, David R. Dowling, “Fluid Mechanics,” 5^th edition, Academic Press, 2012.
• Davidson, P.A., “Turbulence: An Introduction for Scientists and Engineers,” Oxford University Press, 2004.

Evaluation Pattern