Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

Assier, Raphael and Peake, Nigel (2012) Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane. IMA Journal of Applied Mathematics, 77 (5). pp. 605-625.

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Official URL: http://imamat.oxfordjournals.org/content/77/5/605

Abstract

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere.

Item Type: Article
Additional Information: This article is an invitation publication, following the award of the Lighthill-Thwaites prize, awarded for the 2012 Wave Motion paper.
Uncontrolled Keywords: geometrical theory of diffraction acoustic diffraction quarter-plane
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 30 Functions of a complex variable
MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus
MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 43 Acoustics
Depositing User: Dr Raphael Assier
Date Deposited: 08 Dec 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2207

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