# Unit information: Advanced Fluid Dynamics in 2016/17

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Unit name Advanced Fluid Dynamics MATHM0600 20 M/7 Teaching Block 1 (weeks 1 - 12) Professor. Hogg Not open Calculus 2 (MATH 20900), Applied Partial Differential Equations 2 (MATH 20402) None School of Mathematics Faculty of Science

## Description

Unit aims

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

General Description of the Unit

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

## Intended learning outcomes

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.

## Teaching details

A unit of 30 lectures spread over 12 weeks. Regular homework assignments are set.

## Assessment Details

100% 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.