# 2019/20 Taught Postgraduate Module Catalogue

## MATH5458M Advanced Geophysical Fluid Dynamics

### 20 creditsClass Size: 30

Module manager: Dr Sam Pegler
Email: S.Pegler@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2019/20

### 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: 05/11/2019 08:50:05

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