2.25 | Fall 2013 | Graduate

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

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)

Course Info

As Taught In
Fall 2013
Level
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions