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Turbulence and Turbulence Modeling


Credit Hours:


Learning Objective:

The objectives of this course are to provide a sound background in the mathematics and physics of turbulence and to introduce the concepts and tools needed in using and developing turbulence models and turbulence simulation methods.


The course is broken into two parts. The first half covers basic theoretical and physical descriptions of turbulence. In the second half a wide range of turbulence models and simulation methods are presented and discussed. Topics include turbulence models typically used in commercial CFD codes as well as current research approaches.
Spring 2019 Syllabus

Topics Covered:

I. Background on Turbulence: Description of turbulence, Kinmatics of fluid motion, Reynolds averaged Navier-Stokes (RANS) equations, Scaling of turbulent flows (free shear layers and boundary layers), Spectra and two-point correlations II. Turbulence Modeling: Hierarchy of turbulence simulations, Algebraic models, One-equation models, Two-equation models, Modeling compressible flows, Reynolds stress models, Probability density function (PDF) methods, Direct numerical simulation (DNS), Large-eddy simulation (LES), Detached eddy simulation (DES)/Hybrid RANS-LES approaches.


Graduate or senior-level course(s) in fluid mechanics including derivation of the Navier-Stokes equations, potential flow, exact solutions for simple viscous flows, boundary layers and vortex dynamics. Working knowledge of vector calculus, Cartesian tensor index notation (handouts available), and Fourier transforms. Ability to program in Matlab or use CFD and other software may be needed depending on the project topic chosen.

Applied / Theory:

10 / 90

Web Address:

Web Content:

Syllabus, grades, lecture notes, homework assignments and solutions.


There will be approximately 5-6 homework assignments before the midterm exam. It is expected that the homework will require 10-15 hours each. There may be a few additional homework assignments after the exam. Email homework to (PDF files preferred). 30% of course grade.


Individual project having to do with some aspect of turbulence modeling, simulation or theory. Project consists of weekly progress reports, final written report and oral presentation (PowerPoint/PDF slides and 15 minute oral presentation to instructor by phone); 50% of course grade. Topics can be suggested by students, but approved by instructor. The project may be job related, but it does not have to be.


One midterm (2 hours): closed book and closed notes, however an equation and formula sheet is provided; worth 20% of course grade. No Final exam.


Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.

Computer Requirements:

ProEd minimum computer requirements. For the homework students will need to have some type of graphing software so they can plot solutions derived analytically. Students at Purdue typically use Matlab. Matlab is available through ITaP's Go Remote web site. Depending on the project chosen, students may need access to commercial CFD software (such as Fluent), their own in-house codes, a Fortran compiler for working with research codes, and graphics software for post-processing the fluid flow solutions. The midterm exam may require the use of a basic scientific calculator.

Other Requirements:

It may be helpful to have a Purdue career computer account and an Engineering Computer Network (ECN) account with access to AAE department computers.

ProEd Minimum Requirements: