Advanced Fluid Mechanics

Vorticity and Circulation

This section covers lectures 19-20.

Readings

Textbooks

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

• PITCHf/x on Wikipedia. Interesting reference on Magnus force in baseball for those of you who watch baseball or use MLB’s Gameday™ app: Trajectory analysis incorporates the Magnus effect.

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.

Assignment

Problem Set 11

PROBLEMS	SOLUTIONS
Problem 10.2 (PDF)	Solution to Problem 10.2 (PDF)
Problem 10.3 (PDF)	Solution to Problem 10.3 (PDF)
Problem 10.04 (PDF)	Solution to Problem 10.04 (PDF)
Problem 10.05 (PDF)	Solution to Problem 10.05 (PDF)
Problem 10.11 (PDF)	Solution to Problem 10.11 (PDF)
Problem 10.16 (PDF)	Solution to Problem 10.16 (PDF)