Turbulent flows (ME 625)

Objectives of this course are to introduce mathematical formulations, physical insights, and numerical modeling of incompressible turbulent flows.

Instructor: Dr. Sudhakar Yogaraj

Teaching Assistants: Deepak J

Course progress (Spring 2022)

The following is the progress during Spring 2022 semester. The duration of each lecture is 50 minutes.

  • [18/01] Chapter 1: Some famous fluid mechanics experiments, overview of the course

  • [20/01] Motivation, characteristics of turbulent flows

  • [21/01] Are turbulent flows beneficial/detrimental?

  • [25/01] Energy cascade, Introduction to index notation

  • [27/01] Tutorial on index notation. Chapter 2: Need for statistical description, Reynolds decomposition, rules of averaging

  • [28/01] Derivation of Reynolds Averaged Navier-Stokes equations (RANS), Reynolds stress, closure problem

  • [01/02] Mean passive scalar equation, eddy viscosity and gradient-diffusion hypothesis

  • [03/02] Energetics of total- and mean-flow

  • [04/02] Ergodicity hypothesis, Equations for second-order moments of fluctuating velocity

  • [08/02] Turbulent kinetic energy equation

  • [10/02] Review of relevant fluid mechanics concepts, derivation of vorticity equation in index notation

  • [11/02] Vortex stretching mechanism, enstrophy

  • [15/02] Chapter 3: Experimental observations on round jet — velocity profiles, self-similarity, universal constants, entrainment, Reynolds stress

  • [17/02] Turbulent boundary layer approximation, self-similarity solution for plane jet, energy budget

  • [18/02] Simplified TBL approximation and self-similar solutions of Plane wake

  • [22/02] Mean flow equations and velocity profiles in turbulent channel flow

  • [24/02] Friction and Reynolds stresses in channel flow, Pipe flows and effect of roughness

  • [25/02] Chapter 4: Overview of numerical simulations of turbulent flows, Direct numerical simulation

  • [03/03] Hands-on session 1: Introduction to DNSLab. DNS of channel flow, and write mean velocity profile

  • [04/03] Hands-on session 2: Exercises on DNSLab. Q-criterion, and write outputs of turbulence quantities and production

  • [09/03] Mid-semester exam

  • [22/03] Chapter 3 (contd.) Turbulent boundary layers – Mean velocity profiles, van Driest damping function, log-law and power law

  • [24/03] Reynolds stresses in TBL, budgets of normal and shear stresses

  • [25/03] Coherent structures in wall-bounded flows: streaks, streamwise vortices, hairpin vortices, quadrant analysis

  • [29/03] Chapter 4 (contd.) introduction to RANS models, recap of kinetic theory of gases, mixing length hypothesis

  • [31/03] Algebraic models: mixing length, Cebeci-Smith, and Baldwing Lomax models

  • [01/04] Performance of algebraic models in attached and separated flows, Construction of “model” turbulent kinetic energy equation

  • [05/04] Spalart-Allmaras model

  • [07/04] Hands-on session 3: Flow over a NACA0012 airfoil at zero degree AoA with Spalart-Allmaras model using ANSYS-FLUENT

  • [08/04] Hands-on session 3: contd.

  • [12/04] Formulation of k-epsilon and k-omega models

  • [19/04] Hands-on session 4: Flow over a NACA0012 airfoil at 4 degree AoA with Spalart-Allmaras, and other models

  • [21/04] Hands-on session 4: contd. Turbulent flow through a channel and comparison with Johns Hopkins turbulence database

  • [22/04] Performance of two-equation models to free-shear and attached boundary layer flows

  • [26/04] Performance of two-equation models to separated flows, Large eddy simulation

  • [28/04] Term paper presentation

  • [03/05] Term paper presentation

  • [03/05] End-semester exam


  • PA Davidson, Turbulence: An introduction for scientists and engineers, Oxford university press.

  • SB Pope, Turbulent flows, Cambridge university press.

  • J Mathieu, J Scott, An introduction to turbulent flow, Cambridge University Press.

  • H Tennekes, JL Lumley, A first course in turbulence, MIT press.

  • DC Wilcox, Turbulence modeling for CFD, La Canada, CA: DCW industries.

  • V Vuorinen V, K Keskinen DNSLab: A gateway to turbulent flow simulation in Matlab. Comp Phys Comm. 2016.