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General


This course is part of the MAGIC core.

Description

This is offered as a core course for Applied.

Semester

Spring 2019 (Monday, January 21 to Friday, March 29)

Hours

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

Timetable

  • Tue 13:05 - 13:55

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 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.

Lecturer


Jonathan Healey
Email j.j.healey@keele.ac.uk
Phone 01782 733738
Photo of Jonathan Healey


Bibliography


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


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



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%.

Hydrodynamic stability exam

Files:Exam paper
Released: Sunday 28 April 2019 (53.9 days ago)
Deadline: Sunday 12 May 2019 (38.9 days ago)


Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
magic170.pdf
magic171.pdf
magic172.pdf
magic173.pdf
magic174.pdf
magic175.pdf
problemset.pdf


Recorded Lectures


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