A10: Fluid Dynamics and Waves, HT 2008

Lectures: Mon 11.00-12.00 am, Weds 12.00-1.00 pm, Weeks 1-8
Room: Lecture Hall 1, Mathematical Institute
Lecturer: Prof. Tom Witelski
Webpage: http://www.maths.ox.ac.uk/~witelski/a10-2008/ [external]
Webpage: http://www.maths.ox.ac.uk/node/4012/ [official]

Aims and Objectives

This course introduces the mathematical framework used to describe the motion of solids, fluids, and gases. Building on fundamental considerations from geometry, vector calculus, and dynamics, the governing differential equations of motion will be derived. Analytical approaches for solving these equations for simple classes of problems will be developed.

The main themes of the course are

• Kinematics and descriptions of fluid motion. Derivation of the equations of fluid motion. Vorticity, circulation, and theorems for fluid motion and conserved properties. (Weeks 1, 2)
• Two-dimensional inviscid incompressible irrotational flows via complex analysis. Fundamental flows. Motion of irrotational vortices. Construction of flows via the method of images and the Milne-Thomson circle theorem. Construction of flows via conformal mappings. Flows around aerofoils. Blasius' theorems. (Weeks 3--6)
• Water waves and analysis of dispersive wave phenomena. (Weeks 7, 8)

Reading

The primary readings will come from the textbook written by Dr. D. J. Acheson

• Elementary Fluid Dynamics by D. J. Acheson, Oxford University Press

Other reference books

• Theoretical hydrodynamics by L. M. Milne-Thomson
• A first course in fluid dynamics by A. R. Paterson
• Physical fluid dynamics by D. J. Tritton
• Fundamental Mechanics of Fluids by I. G. Currie
• Fluid dynamics for physicists by T. E. Faber

Course materials and external web links

• Problem sheets, supplementary notes and other information will be posted on the Course Materials web page
• Best group velocity and phase velocity links:
  • Java Demo 1
  • Java Demo 2
  • Java Demo 3
  • Wikipedia
• Lecture notes from similar courses
  • Fluid Dynamics at University of London by Burgess and van Elst
  • Fluid Dynamics at Cambridge University by McIntyre
• Fluid Mechanics Film Series at MIT
  Fundamental concepts
  • Flow Visualization
  • Eulerian/Lagrangian descriptions
  • Vorticity
  • Waves in Fluids
  • Pressure fields and fluild acceleration
  Advanced topics: interesting dynamics and properties
  • Rheological Behavior of Fluids
  • Low Reynolds number flow
  • Surface Tension
  • Flow Instabilities
• Potential flow: Nice pages on
  • flow around a cylinder
  • the Joukowski mapping
  • flow around a wing
• Vortex rings: Cool pictures, Cool movies