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Unit of study_

MATH3974: Fluid Dynamics (Advanced)

This unit of study provides an introduction to fluid dynamics, starting with a description of the governing equations and the simplifications gained by using stream functions or potentials. It develops elementary theorems and tools, including Bernoulli's equation, the role of vorticity, the vorticity equation, Kelvin's circulation theorem, Helmholtz's theorem, and an introduction to the use of tensors. Topics covered include viscous flows, lubrication theory, boundary layers, potential theory, and complex variable methods for 2-D airfoils. The unit concludes with an introduction to hydrodynamic stability theory and the transition to turbulent flow.

Code MATH3974
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
An average mark of 65 or more in (12 credit points of MATH2XXX)
Assumed knowledge:
[MATH2961 and MATH2965] or [MATH2921 and MATH2922]

At the completion of this unit, you should be able to:

  • LO1. explain and apply the fundamentals of fluid mechanics
  • LO2. determine how and in what situations a system which is not necessarily liquid can be described as a fluid.
  • LO3. explain and apply the link between Eulerian and Lagrangian descriptions of a fluid.
  • LO4. apply the general theory of asymptotics to simplify equations by exploiting small parameters, scaling regimes and geometric and physical assumptions.
  • LO5. use complex analysis, PDE theory and perturbation theory to describe kinematic and dynamic flows in structured contexts/examples
  • LO6. apply Laplace’s equation to irrotational flow with added circulation and use complex variable methods to solve for two dimensional flow. Explain aerofoil theory and the derivation of the formula for lift.
  • LO7. explain the distinction between and the features of high and low Reynolds number flows.
  • LO8. explain and apply the concepts of hydrodynamic stability
  • LO9. explain the transition to turbulence, the turbulence closure problem and Kolmogorov’s theorem.
  • LO10. explain and apply the fundamental theory of water waves

Unit outlines

Unit outlines will be available 1 week before the first day of teaching for the relevant session.