Unit name | Advanced Fluid Dynamics |
---|---|

Unit code | MATHM0600 |

Credit points | 20 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Professor. Eggers |

Open unit status | Not open |

Pre-requisites |
MATH11009 Mechanics 1, MATH20901 Multivariable Calculus and MATH20402 Applied Partial Differential Equations 2 |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

Understanding the principles governing fluid flow and the mathematical models used to investigate them.

**Unit Description**

The behaviour of ordinary fluids like oil, water, or air can be understood on the basis of a single equation, due to Navier and Stokes. The description of fluid motion thus amounts to finding solutions to the Navier-Stokes equation, a mathematical problem of almost infinite variability and often staggering complexity. (A look at a weather map should convince you of that.) Solutions to physically relevant problems generally involve some approximation, motivated by physical insight, and based on the identification of the key parameters that determine the solution.

Close to an equilibrium state, the problem can be solved by linearising the equation around it. Far away from such a state flows are often characterised by widely differing length scales. This seemingly complex structure can be used to one's advantage by investigating the solution under a change of scales.

Unavoidably, fluid mechanics has broken up into a great number of subfields. However, this course will try to give a more unified view by emphasizing mathematical structures that reappear in different guises in almost all those sub-specialities.

**Relation to Other Units**

This unit is a continuation of the Level 3 Fluid Dynamics unit and an investigation of more advanced topics. This unit is self-contained and it is not necessary to have previously attended Fluid Dynamics. However familiarity with the key themes and ideas of Fluid Dynamics would be advantageous.

Learning Objectives

After taking this unit, students should:

- know the basic equations and the underlying concepts
- realise the importance of the Reynolds number and other non-dimensional parameters
- know how to set up the appropriate mathematical equations for a given flow problem
- appreciate the general concepts of stability and scaling

Transferable Skills

Ability to transfer physical questions into well-defined mathematical problems. Understanding the critical parameters of a problem and developing intuition for the behaviour of a system as a function of these parameters.

The unit will be taught through a combination of

- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours

100% Timed, open-book examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

**Recommended**

- D.J. Acheson,
*Elementary Fluid Dynamics*, Clarendon Press, 1990 - G.K. Batchelor,
*An Introduction to Fluid Mechanics*, Cambridge University Press, 1967 - T.E. Faber,
*Fluid Dynamics for Physicists*, Cambridge University Press, 1995 - L.D. Landau and E.M. Lifshitz,
*Fluid Mechanics*, Pergamon, 1997