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| Module Availability |
| Semester 2 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework (unassessed problem sheets)
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0%
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Test: one assessed problem sheet and a class test
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25%
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Exam (2½ hour unseen paper)
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75%
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Qualifying Condition(s)
A weighted aggregate mark of 50% is required to pass this module.
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| Module Overview |
| By the end of the course the students should understand the concept of hydrodynamic stability in the context of simple parallel flows. They should be able to derive the governing stability differential equations and analyse the stability properties of a range of both inviscid and viscous flows. |
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| Prerequisites/Co-requisites |
| MAT2010 (Fluid Dynamics), MAT2011 (Linear PDEs) and MAT3013 (Mathematics of Weather) |
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| Module Aims |
| The module aims to extend students' knowledge of abstract algebra and their appreciation of the inter-connectedness of the different areas of the subject. |
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| Learning Outcomes |
| Students should acquire a deeper knowledge of groups and rings. They will become familiar with some classical theorems in algebraic structure theory and will have an introduction to algebras and modules. |
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| Module Content |
The content of the module will be split into four areas:
Kelvin-Helmholtz Instability. Inviscid instability of the interface between two parallel flows of different density. This example introduces the notion of linear instability.
Inviscid instability of parallel flows. Derive the Rayleigh equation, examine the stability of piecewise
linear flows, examine the stability criteria for smooth flows, introduce critical layer analysis.
Viscous instability. Derive the Orr-Sommerfeld equation, study the linear stability of plane Poiseuille flow, look at the asymptotic theory in the inviscid limit, and the connection to Rayleigh’s equation.
Boundary layer flows. Uniform flow over a flat plate, flow past a plate with arbitrary slip velocity, stability of boundary layers.
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| Methods of Teaching/Learning |
Lectures: 3 hours lecture/tutorial/examples classes per week for 11 weeks.
Assignment(s): One unassessed piece of coursework, one assessed piece of coursework, and one class test will be set.
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| Selected Texts/Journals |
Recommended text
P. G. Drazin. Introduction to hydrodynamic stability, Cambridge University Press (2002).
Additional reference texts
P. J. Schmid & D. S. Henningson. Stability and transition in shear flows. Springer-Verlag (2001).
P. G. Drazin & W. H. Reid. Hydrodynamic stability, Cambridge University Press (1981).
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| Last Updated |
| 3 May 2011 |
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