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2012/13 Taught Postgraduate Module Catalogue

MATH5457M Advanced Geophysical and Astrophysical Fluid Dynamics

20 creditsClass Size: 30

Module manager: Dr Stephen Griffiths, Prof Onno Bokhove
Email: S.D.Griffiths@leeds.ac.uk, O.Bokhove@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2012/13

Pre-requisite qualifications

(MATH2365 and MATH2620) or MATH3501.

This module is mutually exclusive with

MATH3456	Magnetohydrodynamics
MATH3457	Geophysical and Astrophysical Fluid Dynamics
MATH5456M	Advanced Magnetohydrodynamics

Module replaces

MATH5456M

This module is approved as an Elective

Module summary

This module is concerned with the mathematical modelling of various phenomena observed in geophysical and astrophysical flows. - For geophysical flows, the focus is on wave-like motions in the Earth's atmosphere and ocean, and how these are related to vertical density variations within the fluid and to the rotation of the Earth. - For astrophysical flows, the focus is on how electrically conducting fluids interact with magnetic fields in stellar and planetary interiors, and how this can lead to the generation and maintenance of large-scale magnetic fields, via dynamo action.

Objectives

For students with a basic training in mathematical fluid dynamics, this module will provide the necessary additional knowledge and mathematical techniques to understand and model geophysical and astrophysical flows.

These ideas are central to further study in a range of environmental, climate and solar sciences.

Learning outcomes
1. An awareness of various flow regimes in the Earth's atmosphere and oceans, and in stellar and planetary interiors.
2. An understanding of the underlying physical processes which lead to these flows.
3. The ability to construct and analyse idealized mathematical models of these processes.
4. An appreciation of the relevance and limitations of these mathematical models.
5. Familiarity with more advanced mathematical formulations and techniques for geophysical fluid dynamics, including potential vorticity and quasi-geostrophic dynamics.

Syllabus

1. Governing equations of motion for rotating, stratified flow. Vorticity and potential vorticity.
2. Some effects of rotation: geostrophic flow, Taylor-Proudman theorem, Ekman layers.
3. Rossby waves. Linear wave theory.
4. Shallow-water flows: inertia-gravity waves, Kelvin waves, tides, the wind-driven ocean circulation. Potential vorticity.
5. Some effects of stratification: buoyancy frequency, mountain generated waves. Further linear wave theory. Quasi-geostrophic flow.
6. Derivation of the governing equations of motion for magnetohydrodynamics from Maxwell's equations.
7. Basic properties of the induction equation and the Lorentz force. Alfven's theorem.
8. Discussion of the dynamo problem for the Earth and Sun.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	44	1.00	44.00
Private study hours			156.00
Total Contact hours			44.00
Total hours (100hr per 10 credits)			200.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Student feedback arising from regular problem sheets and workshops.

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	3 hr 00 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 18/01/2013

Disclaimer

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