MTH4341 · Fluid dynamics and turbulence

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 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.

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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.

Workload

• Two 1.5 -hour seminars; • One 1-hour applied class and • 8 hours of independent study per week

Student experience, not official rules. Nothing here changes what the Handbook says.