Programme/Approved Electives for 2021/22
Available as a Free Standing Elective
Level 6 Partial Differential Equations MAT-30003
A `fluid' is anything that flows, like liquids and gasses, and this module 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 wingsThe 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: 1use the method of matched asymptotic expansions to derive dispersion relations for smooth velocity profiles, both with and without viscosity: 1calculate leading-order nonlinear effects on unstable waves: 1determine the propagation properties of unstable waves in shear layers: 1represent flows by piecewise-linear model profiles and derive and analyse their dispersion relations: 1
40 hours lectures and classes.160 hours private study.
1: Exam weighted 100%
Description of Module Assessment
A three-hour, end of module examination.A time constrained invigilated examination on unseen material.