On the diffraction of acoustic waves by a quarter-plane

Assier, Raphael and Peake, Nigel (2012) On the diffraction of acoustic waves by a quarter-plane. Wave Motion, 49 (1). pp. 64-82.

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Abstract

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin�s theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green�s functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin�s third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace�Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two.

Item Type: Article
Uncontrolled Keywords: Quarter-plane Acoustics Diffraction Far-field
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/2206

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