A10: Fluid Dynamics and Waves, HT 2008
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
Course Outline [PDF]
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.
Water waves and analysis of dispersive
wave phenomena. (Weeks 7, 8)
The primary readings will come from the
textbook written by Dr. D. J. Acheson
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