Venue: Online
Class timings: 9 - 10:30 am on Mondays and Wednesdays
First meeting: 12th January 2021

Course description: Following is a course summary but is subject to change depending on students' interests:

  1. Continuum formulation of fluid mechanics, limitations
  2. Lagrangian and Eulerian perspectives 
  3. Conservation of mass (the continuity equation) 
  4. Similarity transforms 
  5. Stream functions, Angular momentum, Velocity gradient tensor – Symmetric and Antisymmetric parts etc. 
  6. Conservation of Momentum – Euler and Navier-Stokes Equations 
  7. Dynamic similarity – Buckingham Pi theorem 
  8. Kelvin’s Circulation theorem 
  9. Couette and Poiseuille Flow 
  10. Introduction to Turbulence – Scaling laws, and energy budget equation 
  11. Fully developed turbulence – K41 hypothesis 
  12. Singular Perturbation Theory 
  13. Bernoulli’s function and principle 
  14. Boundary layer theory 
  15. Flow past a plate, Blasius equation 
  16. Vortex Dynamics 
  17. Use of complex techniques for inviscid, incompressible vortex and mass source induced velocity fields.
  18. Method of images 
  19. Potential flow past a cylinder 
  20. Blasius theorem – Force and torque on a solid body in a fluid (inviscid, incompressible) 
  21. Conformal Mapping 
  22. Flow instabilities – Study of Linearized equations for stability 
  23. Rayleigh Plateau instability 
  24. Orr-Sommerfeld equation 
  25. Benard Problem 
  26. Taylor problem on centrifugal instability 
  27. Reynolds-averaged Navier-Stokes Equations

Evaluation: Homeworks, one midterm, and one final exam.