Wave Mechanics
Co-ordinator: Dr Julius Kaplunov,
OWENS Room 18.03 Maths Blg , Tel x 55806
email:
kaplunov@ma.man.ac.uk
Assessment
|
Credits
|
Contact hours
|
% Exam
|
% Coursework
|
Level
|
|
10
|
24h lectures, 12h tutorials
|
80
|
20
|
M
|
General Description
This course will study aspects
of wave motion arising in many fluidmechanical
systems, and students will be introduced to fundamental ideas such as dispersion,
group velocity, as well as advanced topics including ray theory, non-linear
propagation, shocks, solitary waves. The course will also discuss several
wave systems such as those arising in rotating flows and stratified flows.
Aims
The aim of this course is to introduce
students to aspects of wave motion arising in many fluid mechanical systems.
Objectives
On successful completion of the
course unit students will understand the physical and mathematical reasons
for wave motion and be able to formulate and solve simple problems concerning
the propagation ofwaves in dispersive
and non-dispersive media.
Course content
1. Introduction: wave kinematics.
Phase velocity, group velocity, dispersion, dissipation.
2. Free surface water waves: Standing/progressive
waves, dispersion relations for infinite and finite depthlayers.
Waves in closed containers.
3. Surface tension effects.
4. Waves at a density interface:
Kelvin-Helmholtz instability.
5. Waves in a continuously stratified
fluid: Internal gravity waves.
6. Waves in rotating flows.
7. Sound waves.
8.Introduction
to nonlinear wave propagation. Shallow water theory.Solitary
waves. Shocks waves.
Assessment
Coursework
20% and end of module two-hour closed book examination 80%.
Suggested reading
J.J. Stoker, Water Waves. Wiley,
1958.
M.J. Lighthill, Waves in Fluids.
Cambridge, 1979.
G.B. Whitham, Linear and Nonlinear
Waves. John Wiley, 1974.