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Title: Water-wave propagation through very large floating structures
Authors: Carter, Benjamin
Keywords: Arrays
Linear water waves
Matched asymptotic expansions
Multiple scales
Rayleigh-Ritz
Issue Date: 2012
Publisher: © Benjamin G. Carter
Abstract: Proposed designs for Very Large Floating Structures motivate us to understand water-wave propagation through arrays of hundreds, or possibly thousands, of floating structures. The water-wave problems we study are each formulated under the usual conditions of linear wave theory. We study the frequency-domain problem of water-wave propagation through a periodically arranged array of structures, which are solved using a variety of methods. In the first instance we solve the problem for a periodically arranged infinite array using the method of matched asymptotic expansions for both shallow and deep water; the structures are assumed to be small relative to the wavelength and the array periodicity, and may be fixed or float freely. We then solve the same infinite array problem using a numerical approach, namely the Rayleigh-Ritz method, for fixed cylinders in water of finite depth and deep water. No limiting assumptions on the size of the structures relative to other length scales need to be made using this method. Whilst we aren t afforded the luxury of explicit approximations to the solutions, we are able to compute diagrams that can be used to aid an investigation into negative refraction. Finally we solve the water-wave problem for a so-called strip array (that is, an array that extends to infinity in one horizontal direction, but is finite in the other), which allows us to consider the transmission and reflection properties of a water-wave incident on the structures. The problem is solved using the method of multiple scales, under the assumption that the evolution of waves in a horizontal direction occurs on a slower scale than the other time scales that are present, and the method of matched asymptotic expansions using the same assumptions as for the infinite array case.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/12031
Appears in Collections:PhD Theses (Maths)

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