MAT-40004 - Hydrodynamic Stability Theory
Coordinator: Jonathan J Healey Room: MAC2.12 Tel: +44 1782 7 33738
Lecture Time: See Timetable...
Level: Level 7
Credits: 20
Study Hours: 200
School Office: 01782 733075

Programme/Approved Electives for 2021/22

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

Level 6 Partial Differential Equations MAT-30003

Barred Combinations

None

Description for 2021/22

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.

Aims
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

1: Open Book Examination weighted 100%
A three-hour, end of module examination.
A time constrained online examination on unseen material.