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Water-wave scattering by a periodic array of arbitrary bodies

Published online by Cambridge University Press:  01 February 2006

MALTE A. PETER ,
MICHAEL H. MEYLAN  and
C. M. LINTON
MALTE A. PETER
Affiliation:
Centre for Industrial Mathematics, FB 3, University of Bremen, Germanympeter@math.uni-bremen.de
MICHAEL H. MEYLAN
Affiliation:
Department of Mathematics, University of Auckland, New Zealandmeylan@math.auckland.ac.nz
C. M. LINTON
Affiliation:
Department of Mathematical Sciences, Loughborough University, UKc.m.linton@lboro.ac.uk
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Abstract

An algebraically exact solution to the problem of linear water-wave scattering by a periodic array of scatterers is presented in which the scatterers may be of arbitrary shape. The method of solution is based on an interaction theory in which the incident wave on each body from all the other bodies in the array is expressed in the respective local cylindrical eigenfunction expansion. We show how to calculate the slowly convergent terms efficiently which arise in the formulation and how to calculate the scattered field far from the array. The application to the problem of linear acoustic scattering by cylinders with arbitrary cross-section is also discussed. Numerical calculations are presented to show that our results agree with previous calculations. We present some computations for the case of fixed, rigid and elastic floating bodies of negligible draft concentrating on presenting the amplitudes of the scattered waves as functions of the incident angle.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 548 , 10 February 2006 , pp. 237 - 256
Copyright
© 2006 Cambridge University Press

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