MAGIC014: Hydrodynamic Stability Theory

Course details

A core MAGIC course


Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th


Live lecture hours
Recorded lecture hours
Total advised study hours


13:05 - 13:55


This is offered as a core course for Applied.


It will be assumed that students are familiar with the Navier-Stokes equations. Any previous experience of perturbation methods would be an advantage, but is not essential, as the main ideas will be introduced as needed.


0. Some pictures of unstable flows (motivation)
1. Introduction
The idea of instability
(Approximately) parallel shear flows - e.g. pipe flow, boundary layers, channel flows, jets, wakes, mixing layers
Shear layer stability equations - reduction to linear ODEs
2. Inviscid stability theory
Stability theorems - inflexion points, etc.
Piecewise-linear profiles
Critical points - Tollmien's solutions
Emergence of layered structures in the long-wave limit
Matched asymptotic expansions
Second order long-wave theory capturing critical layers
3. Viscous stability theory
Thin viscous layers within inviscid flow
Destabilizing effects of viscosity
An interpretation of the viscous instability mechanism
4. Weakly nonlinear theory
Solvability conditions - when do solutions to forced equations exist?
Higher order expansions in the amplitude parameter.
Multiple-scales theory.
Amplitude equations - supercritical/subcritical bifurcations.
Wave interactions - resonant and nonresonant cases.
5. Absolute and convective instabilities
Upstream and downstream propagation.
Initial value problems.
Saddle point methods.


  • JH

    Professor Jonathan Healey

    Keele University


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The assessment for this course will be released on Monday 7th May 2018 and is due in by Monday 21st May 2018 at 23:59.

The assessment for this course will be via a single take-home paper made available at the end of the module, with 2 weeks to complete and submit solutions online. Questions may be of different lengths. The number marks for each question will be indicated. The pass mark will be 50%.

Please note that you are not registered for assessment on this course.


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