MAT-40004 - Module Specification
School of Computing and Mathematics
Faculty of Natural Sciences

Programme/Approved Electives for 2020/21

Available as a Free Standing Elective

Co-requisites

None

Prerequisites

Level 6 Partial Differential Equations MAT-30003

Barred Combinations

None

Description for 2020/21

A `fluid' is anything that flows, like liquids and gasses, and this course is concerned with the stability of fluid flows. When a flow is unstable it can become turbulent, which greatly increases fluid mixing and also the aerodynamic drag on a streamlined body. This module will focus on understanding the basic mechanisms that create instability in flows, and on the methods used to calculate the growth rates and length scales of unstable disturbances to a flow. Applications include climate and weather models, fuel mixing in jet and internal combustion engines, and air flow around aircraft wings
The module develops the following Keele Graduate Attributes:
1. an open and questioning approach to ideas, demonstrating curiosity and independence of thought;
2. an appreciation of the development and value of Mathematics, and the links between different areas of the subject;
4. the ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand;
6. the ability to communicate clearly and effectively in written form.

The aims of the module are to introduce students to the branch of fluid mechanics concerned with predicting when disturbances to a given steady flow become amplified, potentially causing a breakdown to turbulence. Attention will be focused on instabilities of shear layers.

Intended Learning Outcomes

prove stability theorems for inviscid shear layers: 1
use the method of matched asymptotic expansions to derive dispersion relations for smooth velocity profiles, both with and without viscosity: 1
calculate leading-order nonlinear effects on unstable waves: 1
determine the propagation properties of unstable waves in shear layers, and calculate when this can produce a global instability: 1
represent flows by piecewise-linear model profiles and
derive and analyse their dispersion relations: 1

Study hours

40 hours lectures and classes.
157 hours private study.
3 hour unseen examination

School Rules

None

Description of Module Assessment