MTH4341 - Fluid dynamics and turbulence - 2019

This unit is an introduction to hydrodynamic stability theory that concerns the stability and instability of fluid flows. Students will be introduced to the theoretical methods required to understand how instabilities develop and how the flow transitions from a laminar to a turbulent state. Instability concepts will be applied to a range of flow systems with applications in biology, geophysics and aerodynamics.

Topics covered include: concepts of linear stability theory; temporal/spatial instabilities; Kelvin-Helmholtz instabilities; capillary instabilities; Rayleigh-Benard instabilities; centrifugal instabilities; inviscid and viscous shear flow instabilities in channels, pipes, cylinders and boundary layers; stability of parallel flows including Rayleigh's equation and inflexion point criteria, Fjortoft's theorem, Squire's theorem and the Orr-Sommerfeld equations; weakly nonlinear theory; coherent turbulent structures.

On completion of this unit students will be able to:

1. Illustrate a deep understanding of hydrodynamic stability theory.
2. Describe and identify the types of instability that form in many physical flows.
3. Derive and explain the significance of Rayleigh's inflexion point criterion, Fjortoft's theorem and Squire's theorem.
4. Summarise the derivation of the Orr-Sommerfeld equation for a given basic state, and undertake a stability analysis.
5. Understand and articulate the physical mechanisms leading to instability and the paths for laminar-turbulent transition.
6. Communicate complex ideas on mathematical treatment of fluid dynamics.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1 hour of tutorial per week
• 8 hours independent study per week

See also Unit timetable information

Master of Mathematics