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