Undergraduate Programme and Module Handbook 2024-2025

# Module MATH4421: Geophysical and Astrophysical Fluids IV

## Department: Mathematical Sciences

### MATH4421: Geophysical and Astrophysical Fluids IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) AND Fluid Dynamics III (MATH3101)

#### Corequisites

- None

#### Excluded Combination of Modules

- None

#### Aims

- To introduce some important ideas in modern fluid dynamics and applied mathematics through the study of fluid systems motivated by geophysical and astrophysical contexts.
- To prepare students for future research in Applied Mathematics.

#### Content

- Equations of geophysical fluid dynamics and common approximations.
- Dynamics of rotating fluids.
- Quasi-geostrophic theory.
- Stratified flow.
- Fluid Instabilities.
- Equations of magnetohydrodynamics (MHD), and their ideal and diffusive limits.
- MHD equilibria: potential, force-free and magnetohydrostatic solutions.
- MHD waves.
- Introduction to dynamo theory.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module, students will:
- be able to solve novel and/or complex problems in Fluid dynamics and MHD.
- have a systematic and coherent understanding of the mathematical formulation behind the geophysical and astrophysical models.
- have acquired a coherent body of knowledge of rotating and stratified fluids and MHD through study of fundamental behaviour of the models as well as specific examples.

Subject-specific Skills:

- Students will develop specialised mathematical skills in mathematical modelling which can be used with minimum guidance.
- They will be able to formulate applied mathematical models for various situations.

Key Skills:

- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and a high level of rigour as well as feedback for the students and the lecturer on the studentsâ€™ progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week in Michaelmas and Epiphany; 2 in Easter | 1 hour | 42 | |

Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany | 1 hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Examination | 3 hours | 100% |

#### Formative Assessment:

Eight assignments to be submitted.

â– Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University