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 (UK)
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.
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
Professor Jonathan Healey
- University
- Keele University
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and 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.
- Introduction to hydrodynamic stability (Drazin, book)
- The theory of hydrodynamic stability (Lin, book)
- Hydrodynamic and hydromagnetic stability (Chandrasekhar, book)
- An introduction to fluid dynamics (Batchelor, book)
- Elementary fluid dynamics (Acheson, book)
- Benard cells and Taylor vortices (Koschmieder, book)
- Pattern formation: an introduction to methods (Hoyle, book)
- Hydrodynamic stability (Drazin and Reid, book)
Assessment
The assessment for this course will be released on Monday 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.
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\%
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\%
Please note that you are not registered for assessment on this course.
Files
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Lectures
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