MAGIC014: Hydrodynamic Stability Theory

Course details

A core MAGIC course


Spring 2023
Monday, January 23rd to Friday, March 31st


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


No bibliography has been specified for this course.


The assessment for this course will be released on Monday 1st May 2023 at 00:00 and is due in before Monday 15th May 2023 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

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


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