Math 812: Fall 2006

Intro to Stability and Turbulence in Shear Flows

Fabian Waleffe

Day  Time  Place 
TR  9:30-10:45pm B317 Van Vleck Hall

Office hours: by appointment.


Advanced Calculus (through Math 321 at least), Differential equations (e.g. Math 319), Linear Algebra (e.g. Math 340), general physics, elementary fluid dynamics, elementary numerical methods (e.g. CS 412), familiarity with Matlab or a programming language (e.g. Fortran, C, C++,...).

REFERENCES: (no textbook required) I'll pick some inspiration from

SUGGESTED READING: (note this is not an endorsement of all of these papers, although most are recommended reading, some are there to test your critical thinking) [I have provided some links, but don't be too lazy and limit yourself to those! do a bit of `research' to get the other papers too]

Navier-Stokes Equations, and a few words about turbulence

NOTE: if you are interested in numerical/mathematical issues, reading the papers above and relevant references therein, and trying to sort out the issues would be a good project for this class. This could be a small group project (2 or 3 people).

Part I: Turbulence Folklore, Inertial (Kolmogorov) scaling

Part II: Turbulence in wall-bounded flows