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Module details for 2022/23.

15 credits

FHEQ Level 7 (Masters)

Module Outline

The aim of this module is to provide an introduction to fluid mechanics, regarded from the perspective of the mathematical analysis of the underlying models in the form of partial differential equations. As such, the content of the module is at the interface between pure and applied mathematics. The module focuses on the basic equations of fluid dynamics, namely the Navier-Stokes and Euler equations. These are the equations governing the motion of fluids such as water or air.
The module will include:
i) An overview of some classical results in fluid mechanics such as: the Hodge decomposition and Biot-Savart laws for vector fields; the theorems of Kelvin, Bernoulli and Helmholtz and the “paradox” of d’Alembert for Euler flows.
ii) A discussion of some simple explicit Navier-Stokes and Euler flows and the roles of viscosity, vorticity and potential functions
iii) An introduction to the modern mathematical theory of the Navier-Stokes and Euler systems including non-classical notions of solutions and general questions of existence and uniqueness of solutions.

Library

1. Majda, A and Bertozzi, A-Vorticity and Incompressible Flow, Cambridge Universitiy Press, 2002
2. Chorin, A and Marsden, J.E. -A Mathematical Introduction to Fluid Mechanics, Springer, 3rd Edition, 1993
3. Doering, C and Gibbon, J.D. -Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, 1995
4.J. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge University Press, 2001

Pre-Requisite

None.

Module learning outcomes

Comprehensively Understand the details of the basic mathematical descriptions of the flow of simple fluids and their key properties.

Comprehensively Understand some classical results in fluid mechanics including their proofs and significance.

Be able to construct some explicit fluid flows and comprehensively understand and be able to apply the theory behind them.

Be able to implement some modern tools in the mathematical analysis of the equations of simple fluids and systematically understand their significance.

View timetable

Timing

Submission deadlines may vary for different types of assignment/groups of students.

Weighting

Coursework components (if listed) total 100% of the overall coursework weighting value.

How to read the week pattern

The numbers indicate the weeks of the term and how many events take place each week.

Dr Gabriel Koch

Convenor, Assess convenor
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