Credits: 3


Prerequisite: ENME331.
Restriction: Permission of ENGR-Mechanical Engineering department.
Also offered as: ENME657.
Credit only granted for: ENME484 or ENME657.
Relentless growth in the speed and size of supercomputers has encouraged the ever expanding use of numerical simulation in the practice of fluids engineering. For the flow past ground vehicles, in the urban grid, re-entering rockets, helicopters landing on ships at sea and countless other examples, the flow is turbulent, and simulation is becoming or will one day become the methodology of choice in analyzing and designing such technologies. The goal of this course is to give an introduction to the analysis of turbulent flow via simulation and the modeling that is used in its development. Among the questions to be considered: What can one hope to learn from flow simulation? What are the strengths of the approach and what obstacles inhibit its application? What kind of physical considerations are required in setting up simulations? How does one analyze the results of a simulation?

Semesters Offered

Fall 2017

Learning Objectives

  • Familiarize  students with turbulent flow simulation.
    • Use simulations to explore the structure and statistics of turbulent flows.
  • Expand your ability to apply mathematics and physics to engineering problems involving fluid mechanics. This is strongly emphasized through lectures and computational assignments.
  • Expand your ability to utilize MATLAB in solving engineering problems.
  • Acquire an ability to critically read research articles in the literature.


Topics Covered

  • Week 1: Preliminaries. What is turbulent flow? Examples of turbulent flow. Goals of studying turbulence.
  • Week 2: Overview of the strategies for predicting turbulent flow.
  • Week 3: Navier-Stokes equation and Reynolds number. What needs to be measured and computed. Averaging. One and two point statistics. Spatial and time spectra.      
  • Week 4: Direct Numerical Simulation (DNS) of  turbulent flow. Requirements for a successful DNS.
  • Week 5: Large Eddy Simulation (LES).
  • Week 6: Using simulation data to predict turbulent motion and analyze its physics. Introduction to the JHU data base and how to access it via MATLAB.
  • Week 7: DNS of isotropic turbulence. Smallest and largest scales. Inertial subrange.
  • Week 8: DNS of channel flow. Setting up first analyses using the JHU database.
  • Week 9: DNS studies of transport phenomena.
  • Weeks 10,11: DNS of channel and boundary layer flows. Observations about velocity and log and power laws and the influence of Reynolds number.
  • Weeks 12,13: Structural analysis of turbulence as revealed in DNS studies.    
  • Weeks 14,15: Results from DNS and LES simulations of complex flow.


Learning Outcomes

  • an ability to apply knowledge of mathematics, science, and engineering
  • an ability to design and conduct experiments, as well as to analyze and interpret data
  • an ability to identify, formulate, and solve engineering problems
  • a recognition of the need for, and an ability to engage in life-long learning

Additional Course Information


Bernard, Peter


None required. Posting of articles on JHU database of turbulent flows.

Class/Laboratory Schedule 

  • Two 75 minute lectures per week
Last Updated By 
Peter Bernard, June 2017