# Semester 2, 2009 - 2010. MA50215 Specialist Reading Course

## The Dynamics of Fluids

This is a reading course in the dynamics of incompressible Newtonian fluids. We begin without viscosity and then go on to consider slow and fast viscous flows. There is a weekly problem sheet and some kind of recommended reading to go with it.

General details of the course are available here.

My syllabus and typed notes borrow heavily from lectures given by Keith Moffatt and typed notes produced by Michael McIntyre (MEM) for the second and third year Cambridge courses in Fluid Dynamics. Of course, any errors are entirely my own contribution.

HEALTH WARNING The notes and problem sheets below are the first versions. They contain typos and errors which were corrected verbally, but which may well not yet be corrected in the TeX files.

So far the contents are roughly as follows:

Week 1: Problem Sheet 1. Discussion on Monday 15 February.
This sheet provides revision of streamlines, particle paths, conservation of mass and Bernoulli's theorem for steady flow.

Suggested reading: MEM's notes, as follows:
Sections 0 and 1: pages 1-11
Section 2: pages 1-2 and 8-11 (sections 2.4 and 2.5)

Week 2: Problem Sheet 2. Discussion on Monday 22 February.
This sheet covers streamfunctions and velocity potentials.

Suggested reading: MEM's notes, as follows:
Sections 0 and 1: pages 13-15
Section 2: pages 1-9

Week 3: Problem Sheet 3. Discussion on Monday 1 March.
This sheet covers the unsteady form of Bernoulli's equation, vorticity, and Kelvin's circulation theorem.

Suggested reading: MEM's notes, as follows:
Section 3: pages 19-20 (section 3.4.4 up to the derivation of (*) ) and page 22 (the derivation of equation (**) )
Section 2: pages 12-18 (sections 2.6 and 2.7). Vorticity and the Circulation Theorem.
Section 3: pages 33-37 (section 3.8). Flow past a cylinder with circulation. Lift.

Week 4: Problem Sheet 4. Discussion on Monday 8 March.
This sheet covers complex potentials.

Acheson, pages 122-127.
Ablowitz and Fokas, pages 32-63 for background on complex differentiability, analyticity, harmonic functions and branch points.

Week 5: Problem Sheet 5. Discussion on Monday 15 March.
This sheet covers flows without inertia: the cases of straight parallel streamlines and circular streamlines, and the use of the biharmonic equation to solve Stokes Equations.

Chapter 2 of my typed notes, pages 1-7.

Week 6: Problem Sheet 6. Discussion on Monday 22 March.
This sheet covers thin films.

Chapter 2 of my typed notes, pages 8-19
Non-examinable 3-page handout on Saffman-Taylor fingering.
Acheson, pages 221-234 and 238-249.

Week 7: Problem Sheet 7. Discussion on Monday 12 April. NOTE THE EASTER BREAK!
This sheet covers the generation and diffusion of vorticity from rigid boundaries.

Chapter 3 of my typed notes.

Week 8: Problem Sheet 8. Discussion on Wed 21 - Fri 23 April sometime TBA. Maybe Wed 21 April at 3pm?
This sheet covers boundary layer flows

Chapter 4 of my typed notes.

Wednesday 5 May (TBC): Revision session.

The typed notes (beware of typos):
Chapter 2

Chapter 3

Chapter 4