# LAGRANGIAN FLUID DYNAMICS OF PLANET EARTH - 2024/5

Module code: MAT3048

## Module Overview

Motivated by problems in meteorology and oceanography, this module applies a range of mathematical techniques to the characteristion of fluid flows. Geometry, vector calculus, differential equations, symmetry, dynamical systems theory, and analysis are all combined with fluid motion to produce a deeper understanding of atmosphere and ocean dynamics.

### Module provider

Mathematics & Physics

### Module Leader

BRIDGES Tom (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 6

### JACs code: G100

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 79

Lecture Hours: 33

Seminar Hours: 5

Captured Content: 33

## Module Availability

Semester 1

## Prerequisites / Co-requisites

MAT2011 Linear PDEs

## Module content

Topics covered will include some or all of:

Kinematics of fluids: Lagrangian particle path formulation; Eulerian formulation; geometry of divergence free vector fields; integral transport theorems.

Dynamical systems aspects of particle motion, mixing and chaotic particle paths.

Kinematics of vorticity; vortex lines, vortex sheets; changes of reference frame; rotating fluids, averaging; Biot-Savart law.

Vortex dynamics on the surface of a sphere, modelling cyclones.

Variational principles for fluid motion; conservation laws; the circulation theorem.

Quasi-geostrophic theory in meteorology

Water wave dynamics in oceanography

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

School-timetabled exam/test | In-semester test (50 min) | 20 |

Examination | Exam (2 hrs) | 80 |

## Alternative Assessment

n/a

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate: Understanding of fundamental concepts and ability to develop and apply them to a new context. Subject knowledge through recall of key definitions, formulae and derivations. Analytical ability through the solution of unseen problems in the test and examination. Thus, the summative assessment for this module consists of: One two hour examination at the end of the semester, worth 80% of the overall module mark one fifty minute class test worth 20% Formative assessment and feedback Students receive written feedback via the marked class test. The solutions to the class tests are also reviewed in the lecture. Un-assessed courseworks are also assigned to the students, and a sketch of solutions to these are provided. Verbal feedback is provided during lectures and office hours.

## Module aims

- The module aims to cover the range of mathematics required to understand the dynamics of fluid motion in the context of meteorology and oceanographic flows on planet earth.

## Learning outcomes

Attributes Developed | ||

001 | Demonstrate understanding of the derivation of the Eulerian and Lagrangian particle path formulation of fluid motion and its kinematics and applications. | K |

002 | Understand the role of vorticity, variational principles, moving frames, rotation and conservation laws in fluid dynamics. | CKT |

003 | Develop the geometry and analysis required for modelling fluid motion | CK |

004 | Understand the stability of fluid flows, from stability of particle motion to stability of Eulerian velocity fields. | CK |

005 | Understand the application of mathematics to the equations of fluid mechanics, with particular attention to equations in meteorology (quasi-geostrophic theory) and oceanography (theory of water waves) | CK |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

Teaching is by lectures, 3 hours per week for 11 weeks. Lecture notes are provided. Learning takes place through lectures, exercises and class tests. Blackboards and whiteboards are used for real-time presentation. Supplementary notes provided via SurreyLearn. Periodic special lectures are devoted to discussion of example sheets.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **MAT3048**

## Other information

n/a

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics with Statistics MMath | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Music BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Financial Mathematics BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.