Lecturer: Thomasina Ball
Term(s): Term 2
Status for Mathematics students: List C
Commitment: 30 lectures
Assessment: 100% Examination
Formal registration prerequisites: None
Familiarity with the mathematical description of fluid dynamics is necessary. It is possible for a strong student to do MA3D1 at the same time: contact the lecturer, if you intend to do it.
Experience with partial differential equations and methods of their solutions.
Some experience of modelling with PDEs. It is particularly important to do MA3J4, if you intend to take MA3D1 Fluid Dynamics at the same time as MA4L0.
Synergies: The following modules would go well with Advanced Topics in Fluids:
- MA3G1 Theory of Partial Differential Equations
- MA3H0 Numerical Analysis and PDEs
- MA4H0 Applied Dynamical Systems
- MA4J1 Continuum Mechanics
Content: The lectures will give students a deeper understanding of the mathematical description of fluid dynamics. They will build on the topics in MA3D1 Fluid Dynamics covering topics from the properties of viscous fluids at low Reynolds number, to instabilities present at the interface between two fluids.
The module will cover the following topics:
- Stokes flow: Properties of Stokes Flows, spherical harmonic solutions, flow around a translating rigid sphere
- Lubrication theory: Thin film approximation, squeeze flows, surface tension, free surface flows
- Complex fluids and non-Newtonian rheology: Constitutive laws for shear thinning, yield stress and viscoelastic fluids, squeeze flows and free surface flows for non-Newtonian rheologies
- Flow through porous media: Darcy's law, flow in a confined and unconfined region, gravity driven flow
- Hydrodynamic instability: The Rayleigh instability, Kelvin-Helmholtz instability
- To provide a useful course for our 1st year PhD students, Master students, DTC students, 4th year MMATHs, Master of Advanced Study (MASt) interested in fluid dynamics related subjects
- Have a module which is flexible enough to adjust to the needs of the current students and to the expertise of available lecturers by choosing a topic from a broad range of interrelated themes.
- Build on entry knowledge towards topics of current interest or research.