Intro to Stability and Turbulence in Shear Flows
Day | Time | Place |
---|---|---|
TR | 9:30-10:45pm | B317 Van Vleck Hall |
Office hours: by appointment.
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]
For further information about the derivation of the Navier-Stokes equations see Chapter 6 in Acheson (especially read the 1st two pages of history) and/or the books by Batchelor (An introduction to fluid dynamics, Cambridge U. Press 1967) or Landau and Lifshitz `Fluid Mechanics', 2nd edition, Pergamon Press (1987) (usually pretty complete but a bit hard to read). The book by R.L. Panton `Incompressible Flow', Wiley 1996 is also quite good and well-known in engineering depts. The first 6 (!) chapters cover the material we reviewed in our first 3 lectures. Although it is called `incompressible flows' it contains good discussions/reviews of the continuum hypothesis, thermodynamics, indicial (or index) notation, vector calculus, etc. Any fluid mechanics book should have a derivation of NSE and a discussion of the Cauchy stress tensor. Yep, this is the same Cauchy as in Cauchy-Riemann, Cauchy's theorem, Cauchy sequences, etc.
Some recent papers on boundary conditions for the Poisson equation for pressure in incompressible flow: