General
This course is part of the MAGIC core.
Description
This is offered as a core course for Applied.
Semester
Spring 2012 (Monday, January 16 to Friday, March 23)
Timetable- Mon 12:05 - 12:55
- Wed 10:05 - 10:55
Lecturers
Chris Jones (main contact)
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David Hughes
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Alastair Rucklidge
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Steven Tobias
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Students
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Ali A
(Loughborough) |
Azwani Alias
(Loughborough) |
Chris Bennett
(Birmingham) |
Matthew Buckley
(Newcastle) |
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Richard Clift
(Loughborough) |
Laura Cole
(Newcastle) |
Sarah Dawson
(Leeds) |
Neil Deacon
(East Anglia) |
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Aiman Elragig
(Exeter) |
Meurig Gallagher
(Birmingham) |
Mariano Galvagno
(Loughborough) |
Sam Jones
(Exeter) |
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Thorpe Maria
(Manchester) |
Pearce Philip
(Manchester) |
Harvind Rai
(Birmingham) |
Chris Rowlatt
(Cardiff) |
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Marjan Safi-Samghabadi
(Durham) |
Francesca Sage-Ling
(Surrey) |
Lucy Sherwin
(Newcastle) |
Jonathan Stone
(Southampton) |
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Julian Thompson
(East Anglia) |
Martin Walters
(East Anglia) |
Michael Walters
(Cardiff) |
James Wright
(Surrey) |
Prerequisites
No prerequisites information is available yet.
Syllabus
- Introduction (2 lectures)
- Derivation of the Navier-Stokes equations
- Boundary conditions
- Non-dimensionalisation
- Additional forces and equations: Coriolis force, buoyancy
- Boussinesq approximation
- Basics of stability theory (2 lectures)
- Swift-Hohenberg equation as a model
- Linear stability. Dispersion relation.
- Marginal stability curve.
- Weakly nonlinear theory.
- Normal form for pitchfork bifurcation
- Global stability
- Rayleigh-Benard convection (4 lectures)
- Basic state. Linear theory. Normal modes.
- Marginal stability curve.
- Weakly nonlinear theory. Modified perturbation theory.
- Global stability for two-dimensional solutions
- Truncation: the Lorenz equations
- Double-diffusive convection (2 lectures)
- Thermosolutal convection. Salt fingers.
- Linear theory: real and complex eigenvalues.
- Rotating convection, plane layer and spherical geometry
- Taylor-Proudman theorem.
- The Taylor-Couette problem (1 lecture)
- Instabilities of parallel flows (6 lectures)
- Instabilities of invicid shear flows. Linear theory.
- Squire's theorem. Rayleigh's equation.
- Plane Couette flow.
- Rayleigh's inflexion point criterion.
- Howard's semi-circle theorem.
- Examples: Kelvin-Helmholtz, bounded shear layer.
- Role of stratification. Role of viscosity, global stability.
- Shear flow instabilities of viscous fluids.
- Orr-Sommerfeld equation.
- Examples: plane Couette flow, plane Poiseuille flow, pipe flow, Taylor-Couette flow.
- Problems with normal mode analysis.
- Pseudo-spectrum and non-normality.
- Absolute and convective instabilities.
- Finite domain effects.
- Introduction to pattern formation (3 lectures)
- Stripes, squares and hexagons. Weakly nonlinear theory.
- Three-wave interactions.
- The role of symmetry.
- Long-wave instabilities of patterns: Eckhaus.
Bibliography
| Hydrodynamic stability | Drazin and Reid |
| Introduction to hydrodynamic stability | Drazin |
| The theory of hydrodynamic stability | Lin |
| Hydrodynamic and hydromagnetic stability | Chandrasekhar |
| An introduction to fluid dynamics | Batchelor |
| Elementary fluid dynamics | Acheson |
| Benard cells and Taylor vortices | Koschmieder |
| Pattern formation: an introduction to methods | Hoyle |
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
No assessment information is available yet.
Assignments
Example sheet 1
| Files: | Exam paper | ||
| Deadline: | Friday 24 February 2012 (453.2 days ago) | ||
Example Sheet 2
| Files: | Exam paper | ||
| Deadline: | Wednesday 7 March 2012 (441.2 days ago) | ||
Example Sheet 3
| Files: | Exam paper | ||
| Deadline: | Wednesday 21 March 2012 (427.2 days ago) | ||
Example Sheet 4
| Files: | Exam paper | ||
| Deadline: | Thursday 12 April 2012 (405.3 days ago) | ||
Files
Files marked L are intended to be displayed on the main screen during lectures.