2024/25 Taught Postgraduate Module Catalogue

MATH5458M Advanced Geophysical Fluid Dynamics

20 creditsClass Size: 50

Module manager: Professor David Hughes
Email: D.W.Hughes@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2024/25

Pre-requisites

MATH3620

Fluid Dynamics 2

This module is mutually exclusive with

MATH3458

Geophysical Fluid Dynamics

This module is approved as an Elective

Module summary

This module is concerned with the mathematical modelling of various phenomena observed in geophysical flows (i.e., those in the Earth's atmosphere and ocean, and upon the planetary surface). The focus is on waves and flowing currents, and how these are related to vertical density variations within the fluid and to the rotation of the Earth.

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 flows. These ideas
are central to further study in environmental and climate sciences.

Learning outcomes
- An awareness of various flow regimes in geophysical fluid dynamics.
- An understanding of the underlying physical processes which lead to these flows.
- The ability to construct and analyse idealized mathematical models of these processes.
- An appreciation of the relevance and limitations of these mathematical models.
- Familiarity with more advanced mathematical formulations and techniques for geophysical fluid dynamics,
including potential vorticity and quasi-geostrophic dynamics.
- Ability to write structured technical reports.

Syllabus

- Governing equations of motion for rotating, stratified flow. Vorticity and potential vorticity.
- Some effects of stratification: buoyancy frequency, gravity waves, mountain generated waves.
- Some effects of rotation: geostrophic flow, Taylor-Proudman theorem, Ekman layers.
- Rossby waves. Linear wave theory.
- Shallow-water flows: inertia-gravity waves, the wind-driven ocean circulation, nonlinear solutions. Potential
vorticity, the Rossby adjustment problem, quasi-geostrophic dynamics.
- Viscous geophysical flows.
- 2D turbulence: conservation laws, inertial ranges.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lectures	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 materials. Completing of assignments and assessments.

Opportunities for Formative Feedback

Student feedback arising from regular problem sheets and example classes.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	10.00
Project	Report and Presentation	30.00
Total percentage (Assessment Coursework)		40.00

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

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	60.00
Total percentage (Assessment Exams)		60.00

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: 29/04/2024 16:16:34

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