Overview
This unit is an introduction to hydrodynamic stability theory that concerns the stability and instability of fluid flows. You 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 … For more content click the Read More button below.
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.
Offerings
S2-01-CLAYTON-ON-CAMPUS
Rules
Enrolment Rule
Contacts
Chief Examiner(s)
Professor Philip Hall
Unit Coordinator(s)
Professor Philip Hall
Notes
This unit is offered in alternate years commencing Semester 2, 2019
Learning outcomes
On successful completion of this unit, you should 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.
Assessment
1 - Continuous assessment
2 - Examination (3 hours and 10 minutes)
Scheduled and non-scheduled teaching activities
Applied sessions
Lectures
Workload requirements
Workload
Availability in areas of study
Master of Mathematics