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| Lecture Room: | B211 Van Vleck Hall |
| Lecture Time: | 9:00–10:15 TR |
| Lecturer: | Jean-Luc Thiffeault |
| Office: | 503 Van Vleck |
| Phone: | (608)263-4089 |
| Email: |
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| Office Hours: | 13:00-14:00 TR, or by appointment. |
Homework 1: Problems 1.2, 1.4, 1.5, and 1.7 from Acheson (p. 23). Due Oct. 2 in class.
Homework 2: Problems 5.1, 5.2, 5.4, and 4.4 from Acheson. Due Oct. 23 in class.
Homework 3: Due Nov. 25 in my mailbox on the second floor of Van Vleck.
1. Redo (properly) the example I did in class: using the image method, find the total force on the solid wall due to a point vortex near a 90 degree corner (use the Blasius formula and the residue theorem). Also find the force if the point vortex is replaced by a point source. Comment on the direction of the force in both cases.
2. Find the complex potential for a vortex near a corner of arbitrary angle α (less than pi), and find the force on the wall. [Hint: use a conformal transformation w=zγ.] Show that your answer reduces to the above image method for a 90 degree corner. For simplicity, you can assume that the vortex is exactly in the center of the corner at a distance a, as shown below.
This course is a broad introduction to fluid dynamics, with an emphasis on equations but always with an eye towards physical insight. We will cover the following topics until time runs out: Continua and conservation laws. Inviscid flow. Irrotational flow. Vorticity. Complex variable methods. Airfoil theory and conformal transformations. Viscosity and the Reynolds number. The limit of zero Reynolds number. Swimming of microorganisms. Thin flows. Instabilities. Everything breaks down: turbulence.
The textbook for the class is D. J. Acheson's Elementary Fluid Mechanics (Oxford University Press). ISBN: 0198596790.
Every two weeks or so I will assign homework from the textbook and post it here.
There will be a final exam. The final grade will be computed according to:
| Homework | 50% |
| Final exam | 50% |
| Final exam | Handed out on December 9 [download it here]; due Tuesday December 16 at 4pm in my mailbox on the 2nd floor of Van Vleck. |
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Last modified: 13:15 7 December 2008 |
Background: Coarsening of a binary fluid (Simulations by Lennon Ó Náraigh) |