MAGIC014: Hydrodynamic Stability Theory

Course details

A core MAGIC course

Semester

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

Hours

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

Timetable

Tuesdays
13:05 - 13:55

Course forum

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Description

This is offered as a core course for Applied.

Prerequisites

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. 

Syllabus

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.

Lecturer

  • JH

    Prof Jonathan Healey

    University
    Keele University

Bibliography

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Assessment

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Recorded Lectures

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