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.

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, 2020

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 summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40%

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

Workload requirements

Workload

Availability in areas of study

Master of Mathematics