Physics of Turbulence

By Prof. Mahendra Verma   |   IIT Kanpur
Learners enrolled: 516
Turbulence is everywhere—in the interiors and atmospheres of planets and stars, galaxies, biological systems including human body, engineering flows, etc. In this course, we will cover fundamental aspects of turbulence—Kolmogorov’s theory of turbulence in spectral and real space; two-dimensional turbulence; energy transfers; enstrophy and kinetic helicity cascades; more complex applications, such as passive scalar, turbulent thermal convection, and magnetohydrodynamic turbulence.

INTENDED AUDIENCE: Any Interested learners
PREREQUISITES:          Basic fluid dynamics, Calculus, Fourier transforms
INDUSTRY SUPPORT:   Companies working in CFD, turbulence
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Start Date : 29 Jul 2019
End Date : 18 Oct 2019
Exam Date : 16 Nov 2019 IST
Category :
  • Physics
Credit Points : 3
Level : Undergraduate

Course layout

Week 1: Introduction; Basic equations of hydrodynamics in real space; Conservation laws
Week 2: Fourier Space Description of Hydrodynamics;
Week 3: Fourier description contd. Craya-Herring basis
Week 4: Instabilities
Week 5: Saturation of nonlinearity; Patterns
Week 6: Energy transfers in fluid flows
Week 7: Kolmogorov’s theory of turbulence (in Fourier space)
Week 8: Kolmogorov’s theory of turbulence (in real space)
Week 9: Enstrophy; Two-dimensional turbulence; Kinetic helicity
Week 10:Turbulence with a scalar; Passive scalar;
Week 11:Turbulent thermal convection
Week 12:Turbulence with a vector; Magnetohydrodynamic turbulence

Books and references

1. M. K. Verma, Energy transfers in Fluid Flows, Cambridge Univ. Press, 2019
2. M. K. Verma, Physics of Buoynat Flows, World Scientific, 2018
2. S. B. Pope, Turbulent Flows, Cambridge Univ. Press, 2000.

Instructor bio

Prof. Mahendra Verma received his Ph.D. degree from University of Maryland. Presently he is a Professor at the Physics Department of Indian Institute of Technology Kanpur, India. He is a recipient of Swarnajayanti fellowship, INSA Teachers Award, and Dr. A.P.J. Abdul Kalam Cray HPC Awards. He authored the books “Introduction to Mechanics”, “Physics of Buoyant Flows: From Instabilities to Turbulence”, and “Energy Transfers in Fluids Flows: Multiscale and Spectral Perspectives”. His research interests include turbulence, nonlinear dynamics, high-performance computing, and non-equilibrium statistical physics. He and his group have developed a spectral code TARANG that can simulate variety of fluid flows.

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: 16 November 2019, 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.

  • 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

  • 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 Kanpur. It will be e-verifiable at nptel.ac.in/noc.
  • Only the e-certificate will be made available. Hard copies are being discontinued from July 2019 semester and will not be dispatched

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