Vorticity and Circulation

This section covers lectures 19-20.



Reading in: Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 6th ed. Academic Press, 2015. ISBN: 9780124059351.

  • Chapter 5: Vorticity Dynamics
    • 5.1: Introduction
    • 5.2: Kelvin's Circulation Theorem
    • 5.3: Helmhotz's Vortex Theorems
    • 5.4: Vorticity Equation in a Nonrotating Frame
    • 5.8: Vortex Sheet
  • Chapter 6: Ideal Flow
    • 6.5: Forces on a Two-Dimensional Body; Blasius Theorem; Kutta-Zhukhovsky Lift Theorem

Additional Readings

Videos Seen During Class

  • torenheksje. "Dolphins Blow Bubble Air Rings." January 25, 2008. YouTube. https://youtu.be/bT-fctr32pE
    YouTube has a number of great links of dolphins & beluga playing with vortex rings; clearly they are masters of Kelvin's Theorem.
  • thegreidy. "Fellowship of the Ring Smoke Galleon Scene." May 30, 2008. YouTube. https://youtu.be/UdE0qjbwwWo
    This guy must have been friends with Lord Kelvin (even looks like him a bit!). Clearly an expert in control of circulation.


Problem Set 11