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MATH44120: Geophysical and Astrophysical Fluids

It is possible that changes to modules or programmes might need to be made during the academic year, in response to the impact of Covid-19 and/or any further changes in public health advice.

Type Tied
Level 4
Credits 20
Availability Available in 2024/2025
Module Cap None.
Location Durham
Department Mathematical Sciences

Prerequisites

  • Analysis in Many Variables and Fluid Dynamics

Corequisites

  • None

Excluded Combinations 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.
  • 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 students progress.
  • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week in Michaelmas and Epiphany; 2 in Easter1 hour42 
Problems Classes8Fortnightly in Michaelmas and Epiphany1 hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
End of year written examination3 hours100 

Formative Assessment

Eight written assignments to be assessed and returned. Other assignments are set for selfstudy and complete solutions are made available to students.

More information

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