Module manager: David Hughes
Email: d.w.hughes@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2026/27
MATH3400 Fluid Dynamics
| MATH3400 | Fluid Dynamics |
MATH 3459 (5459) Astrophysical Fluid Dynamics (and advanced variant) MATH 3458 (5458) Geophysical Fluid Dynamics (and advanced variant)
This module is not approved as an Elective
This module concerns mathematical modelling of various phenomena observed in astrophysical and geophysical flows, specifically those in planetary and stellar atmospheres and interiors; applications include the modelling of the climate and of space weather. The focus is on understanding key dynamical processes in such flows, including, for example, those due to rotation and density stratification, and, in many astrophysical flows, the electrical conductivity of the fluid (which can thus support a magnetic field). These effects lead to a wide range of interesting waves and instabilities, with physical and observational significance.
Students will learn of the physical motivation behind some of the most interesting problems in astrophysical and geophysical fluid dynamics, through discussions of the physics in planetary interiors and atmospheres and in stellar interiors. They will learn how important constraints – imposed by, for example, density stratification, rapid rotation or a strong magnetic field – can be incorporated into modified forms of the governing equations (e.g., the shallow water equations). Students will learn the general theory of waves and instabilities and then apply these techniques to understand observed astrophysical and geophysical phenomena.
On successful completion of the module students will be able to: 1. Understand the governing equations needed to describe astrophysical and geophysical fluid dynamics, including the effects of compressibility and magnetic fields. 2. Formulate mathematical models of fluid flows in various astrophysical and geophysical contexts – for example, the shallow water and quasi-geostrophic equations. 3. Linearise the governing equations and consider the nature of any resulting wave motions and instabilities, and their relevance in astrophysical and geophysical contexts.
1. Introduction to fluid dynamical phenomena in geophysical and astrophysical contexts. 2. Derivation of the various governing equations. For geophysics, the equations of rotating, stratified flow. For astrophysics, the equations of compressible fluids and the equations of electrically conducting fluids (magnetohydrodynamics or MHD). 3. Investigation of the key effects of stratification and rotation (e.g. buoyancy frequency, geostrophic flow, Taylor–Proudman theorem). 4. Investigation of the fundamental properties of the MHD equations. 5. Waves in astrophysical and geophysical fluid dynamics: gravity waves, Rossby waves, sound waves, Alfvén waves. 6. Instabilities in AGFD: e.g. convective instability, shear flow instability, magnetic buoyancy instability. 7. A discussion of the role of AGFD in climate modelling and in modelling space weather, with implications for the terrestrial climate 8. Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar: shallow water flows in astrophysics and geophysics; accretion flows and accretion discs; dynamos in stars and planets; introduction to turbulence.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lectures | 33 | 1 | 33 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 12/05/2026
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