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Essentials of Turbulence

By Prof. Abhilash J. Chandy   |   IIT Bombay
Learners enrolled: 316   |  Exam registration: 54
ABOUT THE COURSE:

Turbulence is a complex and fascinating phenomenon that plays a crucial role in various scientific and engineering disciplines, from aerodynamics and meteorology to astrophysics and industrial flows. This course provides a comprehensive introduction to turbulence, covering its fundamental principles, mathematical modeling, and practical applications. By the end of the course, students will have a solid foundation in turbulence theory and its mathematical aspects.

Course Objectives:
  • Understand the physical nature of turbulence and its significance in fluid dynamics.
  • Explore the governing equations of turbulent flows, including the Navier-Stokes equations.
  • Learn about statistical and spectral descriptions of turbulence.
  • Analyze turbulence modeling approaches, such as Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS).

INTENDED AUDIENCE: Mtech/PhD students, Thermal and Fluid Engineers

PREREQUISITES: Prerequisite degree: BTech
Prerequisite courses: Fluid Mechanics, Engineering Mathematics

INDUSTRY SUPPORT: ANSYS, GE, Airbus, Tata motors, Boeing, DRDO, ISRO, HAL, Shell and other companies working in CFD
Summary
Course Status : Ongoing
Course Type : Elective
Language for course content : English
Duration : 12 weeks
Category :
  • Mechanical Engineering
  • Computational Thermo Fluids
  • Propulsion
Credit Points : 3
Level : Postgraduate
Start Date : 19 Jan 2026
End Date : 10 Apr 2026
Enrollment Ends : 02 Feb 2026
Exam Registration Ends : 20 Feb 2026
Exam Date : 17 Apr 2026 IST
NCrF Level   : 4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits



Course layout

Week 1:  Fundamental considerations of turbulence
  • The "despair" in turbulence
  • Why Study Turbulence?
  • Descriptions of turbulence: How to define turbulence?
  • A brief history of turbulence
  • Eras of turbulent studies

Week 2: The nature of turbulence
  • Irregularity, Diffusivity, Large Reynolds numbers, 3D vorticity fluctuations, dissipation
  • Methods of analysis
  • Origin of turbulence
  • Diffusivity of turbulence
  • Length scales in turbulent flows

Week 3: Equations of fluid motion
  • Nature of turbulent flows
  • Continuity and momentum equations
  • Role of pressure and conserved scalars; vorticity equation
  • Rates of strain and rotation; transformation properties
  • Reynolds number similarity

Week 4: Statistical description of turbulent flows
  • Random nature of turbulence
  • Characterization of random variables; Examples of PDF
  • Joint random variables; Joint PDFs; Conditional PDFs
  • Random processes; Statistically Stationary Random Processes
  • Statistical Stationarity and homogeneity; Wavenumber spectra

Week 5: Mean flow equations
  • Reynolds equations
  • Closure problem
  • Anisotropy
  • Gradient diffusion hypothesis
  • Turbulent viscosity hypothesis

Week 6: Scales of turbulent motion Part A
  • Energy cascade
  • Kolmogorov hypotheses Part 1
  • Kolmogorov hypotheses Part 2
  • Energy Spectrum Part 1
  • Energy Spectrum Part 2

Week 7: Scales of turbulent motion Part B
  • Fourier modes
  • Fourier series representation
  • Projection Tensor
  • The evolution of Fourier modes
  • The kinetic energy of Fourier models

Week 8: Scales of turbulent motion Part C
  • Velocity spectrum tensor
  • Energy spectrum function
  • Kolmogorov spectra
  • Model spectra
  • Dissipation spectra

Week 9: Modeling and simulation

  • Challenges and modeling approaches Part 1

  • Challenges and modeling approaches Part 2
  • Modeling cost and ease of use
  • Direct Numerical Simulation: Pseudo-spectral methods Part 1
  • Direct Numerical Simulation: Pseudo-spectral methods Part 2
Week 10: Modeling and simulation

  • Direct Numerical Simulation: Computational cost Part 1
  • Direct Numerical Simulation: Computational cost Part 2
  • Turbulent Viscosity Models

Large Eddy Simulations
  • Filtering
  • Spectral representation

Week 11: Large Eddy Simulations

  • Resolution of filtered fields Part 1
  • Resolution of filtered fields Part 2
  • Filtering rate of strain
  • Smagorinsky model Part 1
  • Smagorinsky model Part 2


Week 12: 

  • Practice Problems Part 1

  • Practice Problems Part 2
  • Practice Problems Part 3
  • Practice Problems Part 4
  • Practice Problems Part 5

Books and references

• Turbulent Flows, Stephen B. Pope.
• A First Course in Turbulence, Tennekes and Lumley
• Turbulence: An introduction for scientists and engineers, P.A. Davidson

Instructor bio

Prof. Abhilash J. Chandy

IIT Bombay
Prof. Abhilash Chandy received his Doctoral degree in Mechanical Engineering from Purdue University in West Lafayette, Indiana, in 2007. After more than a year of working as a postdoctoral researcher at Purdue, in 2008, he joined the Mechanical Engineering department of University of Akron, Akron, Ohio, as a tenure-track Assistant Professor and was tenured and promoted to Associate Professor in 2014. In 2017, he joined the Indian Institute of Technology Bombay, as an Associate Professor and later was promoted to full Professor in 2021. His research interests include thermo-fluid sciences, computational fluid dynamics (CFD), turbulence and manufacturing process modelling. He has been involved in teaching a variety of courses in Fluid Mechanics, Heat Transfer, Engineering Mathematics, Gas Dynamics and Turbulence.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: April 17, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team
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