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 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. Further applications include atmospheric and oceanic flows in climate and weather models, fuel mixing in jet and internal combustion engines, and air flow around aircraft wings. This module will focus on understanding the basic mechanisms that create instability in flows, and on methods used to calculate the growth rates and length scales of unstable disturbances to a flow so as to explain observed phenomena.
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, and calculate when this can produce a global instability: 1represent flows by piecewise-linear model profiles andderive and analyse their dispersion relations: 1
40 hours lectures and classes.157 hours private study.3 hour unseen examination
1: Open Book Examination weighted 100%
Description of Module Assessment
A three-hour, end of module examination.A time constrained online examination on unseen material.