## Module and Programme Catalogue

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## MATH3458 Geophysical Fluid Dynamics

### 15 creditsClass Size: 30

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

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24

### Pre-requisites

 MATH3620 Fluid Dynamics 2

### This module is mutually exclusive with

This module is approved as a discovery module

### 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 that 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.

### Syllabus

- Governing equations of motion for rotating, stratified flow. Vorticity.
- Some effects of stratification: buoyancy frequency, gravity waves.
- Some effects of rotation: geostrophic flow, Taylorâ€“Proudman theorem, Ekman layers.
- Rossby waves. Linear wave theory.
- Shallow-water flows: inertia-gravity waves, the wind-driven ocean circulation, nonlinear solutions.
- Viscous geophysical flows.
- 2D turbulence: conservation laws, inertial ranges.

### Teaching methods

 Delivery type Number Length hours Student hours Lectures 33 1.00 33.00 Private study hours 117.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 150.00

### 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

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