## Viscous flow

Web address:
**http://www.maths.ox.ac.uk/~fowler/courses/viscous.html**

#### Class times

Monday 4,5, weeks 3-8 (Sam Howison) in DH seminar room.

Tuesday 10, weeks 3-8 (John Coats)
### Synopsis

- Material derivative, transport theorem, mass conservation,
incompressibility.
- Vectors, tensors, summation convention. Stress tensor, rate of
strain tensor.
- The general linear, isotropic viscous fluid. Navier-Stokes
equation.
- Boundary conditions. Exact solutions: plane Poiseuille,
Hagen-Poiseuille, Stokes,
Taylor-Couette flows.
- Jeffery-Hamel
flow.
- The energy equation.
- Dimensional analysis, Reynolds
number.
- Stream function, vorticity, high Reynolds number flow.
Prandtl-Batchelor theorem.
- Thermal and viscous boundary layers. Prandtl's boundary layer equations.
- Blasius flow, similarity solutions. Separation.
- Wakes, theory of flight.
- Instability and turbulence.
- Slow flow, Stokes equations.
- Oseen approximation.
- Lubrication theory, slider bearing and squeeze film.
- Glaciers and ice sheets.

### Reading

- H. Ockendon and J.R. Ockendon 1995 Viscous flow. C.U.P.,
Cambridge.
- D.J. Acheson 1990 Elementary fluid dynamics. O.U.P., Oxford.
- M.E. O'Neill and F. Chorlton 1989 Viscous and compressible fluid
dynamics. Ellis Horwood, Chichester (out of print).

#### Further reading

- C.J. Adkins 1983 Equilibrium thermodynamics, 3rd edition. C.U.P.
- G.K. Batchelor 1967 An introduction to fluid dynamics. C.U.P.
- H. Schlichting 1979 Boundary-layer theory, 3rd ed. McGraw-Hill,
New York.

### Course materials

These can be downloaded as postscript or pdf files.