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, 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 summary

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

Continuous assessment: 40%

Hurdle requirement: If you would otherwise have passed the unit but who do not achieve at least 45% of the marks available for the end-of-semester examination will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. If you are3 enrolled in MTH5341 you will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4341. The assignments and exam in this unit will use some common items from the MTH4341 assessment tasks, in combination with several higher level questions and tasks.

Workload requirements

Workload