Thesis-2002-Ratcliffe.pdf (4.43 MB)
Trapped modes in the presence of thin obstacles
thesis
posted on 2018-09-05, 11:39 authored by Keith RatcliffeIn this thesis we use various techniques to investigate the occurrence of trapped modes in
the presence of thin obstacles. Physically trapped modes are oscillations of finite energy
in a fluid which is unbounded in at least one direction. These oscillations mainly occur
locally to some structure and decay to zero at large distances away from it. Trapped
modes are important as they have been found to exist in a wide range of physical
situations.
We consider a number of problems in two and three dimensions including waveguides
containing bodies and arrays of identical structures. A modified residue calculus
technique, a variational technique and a method based on the truncation of matched
eigenfunction expansions are used to solve the problems, with numerous results presented.
Funding
Engineering and Physical Sciences Research Council (award no.: 98316228).
History
School
- Science
Department
- Mathematical Sciences
Publisher
© K. RatcliffePublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2002Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en