MA4L015 Advanced Topics in Fluids
Introductory description
Fluid dynamics forms a core subject with applications in a number of disciplines including, engineering, nanotechnology, biology, medicine and geosciences. Principles of fluid dynamics serves as an anchor to describe natural phenomena by providing a common language and set of tools for describing, analyzing and understanding observations and experiments in such a diverse array of disciplines. Continuing on from MA3D1: Fluid dynamics, in this module we will study selected advanced topics in fluid dynamics that provides a core understanding of fluid dynamics phenomena.
Module aims
 Students will be able to apply the governing principles of fluid dynamics to specific phenomena, possibly involving some systematic simplification methods.
 They will be introduced to some advanced techniques for analyzing fluid flow.
 They will be able to related observations in nature to the aforementioned analysis techniques.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Vorticity dynamics
 Complex fluids and nonNewtonian rheology
 Lubrication theory
 Stokes flow
 Hydrodynamic stability
 Computational fluid dynamics
 Flow through porous media
 Turbulence
Learning outcomes
By the end of the module, students should be able to:
 Apply and/or simplify the partial differential equations governing fluid flow.
 Solve the derived equations.
 Be able to translate the solution into a physical intuition for the underlying flow phenomenology.
Interdisciplinary
Fluid dynamics is a subject of interest in fields ranging from astronomy to nanotechnology in scale, and from medicine to engineering in application. The common framework provided by fluid dynamics binds the practitioners in a fellowship that transcends these disciplines.
Subject specific skills
Ability to apply and simplify the equations governing fluid flow.
Ability to model physical systems involving fluid flow.
Develop familiarity with different kinds of fluids.
Transferable skills
Ability to interpret observations and propose candidate explanations. Ability to translate scientific ideas into mathematical language and back. Ability to think creatively. Ability to discern the validity of a proposed explanation.
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Private study  117 hours (80%) 
Total  147 hours 
Private study description
Homework problems.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B1
Weighting  Study time  

Inperson Examination  100%  3 hours 
Standard 3 hour written exam.

Feedback on assessment
Written feedback on the outcome of the exam.
Courses
This module is Optional for:
 Year 1 of TMAAG1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 1 of TMAAG1P0 Postgraduate Taught Mathematics
 Year 1 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
This module is Option list A for:
 Year 2 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 2 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)

UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 4 of FG31 Mathematics and Physics (MMathPhys)
 Year 4 of FG31 Mathematics and Physics (MMathPhys)
 Year 4 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 5 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:
 Year 2 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 2 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
 Year 4 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 3 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 4 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list C for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 4 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe