MAGIC014: Hydrodynamic Stability Theory

Course details

A core MAGIC course


Spring 2021
Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th


Live lecture hours
Recorded lecture hours
Total advised study hours


13:05 - 13:55 (UK)


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 layersShear layer stability equations - reduction to linear ODEs

2. Inviscid stability theory Stability theorems - inflexion points, etc.Piecewise-linear profilesCritical points - Tollmien's solutionsEmergence of layered structures in the long-wave limitMatched asymptotic expansionsSecond order long-wave theory capturing critical layers

3. Viscous stability theory Thin viscous layers within inviscid flowDestabilizing effects of viscosityAn 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 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.

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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