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This course is part of the MAGIC core.


This is offered as a core course for Applied.


Spring 2020 (Monday, January 20 to Friday, March 27)


  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40


  • Tue 13:05 - 13:55


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.

Other courses that you may be interested in:


Jonathan Healey
Phone 01782 733738
Photo of Jonathan Healey


Hydrodynamic stabilityDrazin and Reid
Introduction to hydrodynamic stabilityDrazin
The theory of hydrodynamic stabilityLin
Hydrodynamic and hydromagnetic stabilityChandrasekhar
An introduction to fluid dynamicsBatchelor
Elementary fluid dynamicsAcheson
Benard cells and Taylor vorticesKoschmieder
Pattern formation: an introduction to methodsHoyle


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