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Course Specifications


Textbook: None


Instructor : Goodarz Ahmadi (CAMP 267, 268-2322) 
Office Hours: Monday and Wednesday 1:00 - 3:30 p.m. 


Course Site: 


Prerequisites: ME 527  



Course Learning Objectives

  1. To provide the students with a fundamental understanding of turbulent flows.
  2. To familiarize the students with the stochastic and chaotic nature of turbulence. 
  3. To provide the students with the tools for modeling turbulent flows. 
  4. To familiarize the students with the statistical theories of turbulence.
  5. To familiarize the student with simulation techniques in turbulent flows.
  6. To familiarize the students with applications of turbulence in industry and environment.

Course Learning Outcomes


Objective 1:

  • Students will become familiar with fundamental physics of turbulent flows. Students will become familiar with transport of moment, energy and vorticity in turbulent flows.

Objective 2:

  • Students will be able to analyze simple shear, wall bounded and boundary layer flows with the use of phenomenological models of turbulence.  Students will become familiar with recent and advanced higher order modeling of turbulent shear flows.  Students will be able to analyze turbulent flows in complex regions with the use of commercial codes.

Objective 3:

  • Students will become familiar with the direct and large-eddy simulation of turbulent flows.  Students will become familiar with the classical and modern statistical theories of turbulence.

Objective 4:

  • Students will perform stochastic simulations in their respective fields of interest. Students will become familiar with the applications of turbulence in industry and environment.


Course Outline




IV. TURBULENCE MODELING                  - Eddy Viscosity
                 - Mixing Length Hypothesis,   (Slides)                  - k-e Models
                 - Stress Transport Models,  (Slides)
                 - Higher-Order Modelings,  (Slides)
                 - Thermodynamical Approach to Modeling,  (Slides)

  • Computational Modeling of Turbulence
                - Commercial codes (FLUENT)                 - Subgrid-Scale Modeling
  • Homogeneous Isotropic Turbulence
               - Karman-Howarth Equations               - Lundgren's Theory
              - Chung's Kinetic Theory of Turbulence
              - Pope's pdf Model               - Orthogonal Basis
              - First Order System
              - Navier-Stokes System
              - Low Dimensional Dynamical System
              - Applications to Modeling               - Orthogonal Random Functions
              - Meecham's Theory
  • Kraichnan's Direct Interaction Theory
             - Infinitesimal Impulse Response
             - Eulerian Direct Interaction Approximation
  • Functional Approach
            - Hopf's Characteristic Functional Theory of Turbulence
            - Lewis-Kraichnan Approach
  • Stochastic Methods
           - Coherent Structures
           - Wavelet Transform
           - Stochastic Estimation
           - Pseudo-Flow Visualization



Evaluation Methods

  • Homework 10% 
  • Exam-1   25%    March 4, CAMP 177
  • Exam-2   35%    Final Exam Week  
  • Project 1   10%  February 11
  • Project 2   20% April 19


Course Description

  ME 639 Advanced Turbulence R-3, C-3. 
Prerequisites: ME 527 or equivalent. 

Review of viscous flow theory. Review of instability of viscous flows. Origin of turbulence. Phenomenological theories of turbulence. Reynolds' equation. Energy budget and vorticity dynamics in turbulence. Free shear and internal flows. Turbulent boundary layer. Introduction to turbulence modeling. The k-e and stress transport models.  Recent developments in turbulence modeling, stress transport models, multipoint closure methods, and thermodynamical formulation. Turbulent diffusion, isotropic turbulence and Karman-Howarth equation. Kraichnan's direct interaction approximation.Wiener-Hermite expansion approach. Characteristic functional formulation and Hopf's theory. Lundgren's probabilistic formulation and Chung's kinetic theory of turbulence. Direct and Large-Eddy simulation techniques. Proper orthogonal decomposition Techniques. Chaos and dynamical systems, stochastic Estimation, Lagrargian mean approaches.



Exam & Homework Policies


Exam Policy


Exams will be open book.


Homework Policy


Homework will be collected as assigned.  Homework will be graded and returned to the students. 



| CRCD | ME 326 | ME 437 | ME 529 | ME 537 | ME 637 | ME 639 |
Turbulence & Multiphase Fluid Flow Laboratory | Goodarz Ahmadi | Department of Mechanical & Aeronautical Engineering | School of Engineering
Copyright © Goodarz Ahmadi. All rights reserved. Potsdam, New York, 13699