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:
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
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.
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