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Water-wave scattering by a semi-infinite periodic array of arbitrary bodies

  • MALTE A. PETER (a1) and MICHAEL H. MEYLAN (a2)

We consider the scattering by a semi-infinite array of bodies of arbitrary geometry excited by an incident wave in the linear water-wave formulation (which reduces to the simpler case of Helmholtz scattering if the depth dependence can be removed). The theory presented here is extremely general, and we present example calculations for an array of floating elastic plates (a highly non-trivial scatterer). The solution method follows closely from the solution for point scatterers in a medium governed by Helmholtz's equation. We have made several extensions to this theory, considering water-wave scattering, allowing for bodies of arbitrary scattering geometry and showing how to include the effects of bound waves (called Rayleigh–Bloch waves in the water-wave context) in the formulation. We present results for scattering by arrays of cylinders that show the convergence of our methods and also some results for the case of scattering by floating elastic plates and fixed docks.

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Abramowitz M. & Stegun I. A., (Eds.) 1970 Handbook of Mathematical Functions. Dover.
Hills N. L. & Karp S. N. 1965 Semi-infinite diffraction gratings I. Comm. Pure Appl. Maths 18, 203233.
von Ignatowsky, W. 1914 Zur Theorie der Gitter. Ann. Phys. 44, 369436.
Kagemoto H. & Yue D. K. P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189209.
Linton C. M. 1998 The Green's function for the two-dimensional Helmholtz equation in periodic domains. J. Engng Maths 33, 377402.
Linton C. M. 2006 Schlömilch series that arise in diffraction theory and their efficient computation. J. Phys. A: Math. Gen. 39, 33253339.
Linton C. M. & Evans D. V. 1993 The interaction of waves with a row of circular cylinders. J. Fluid Mech. 251, 687708.
Linton C. M. & Martin P. A. 2004 Semi-infinite arrays of isotropic point scatterers. A unified approach. SIAM J. Appl. Maths 64 (3), 10351056.
Linton C. M. & McIver M. 2002 The existence of Rayleigh-Bloch surface waves. J. Fluid Mech. 470, 8590.
McIver P. 2002 Wave interaction with arrays of structures. Appl. Ocean Res. 24, 121126.
Meylan M. H. 2002 Wave response of ice floes of arbitrary geometry. J. Geophys. Res. – Oceans 107 (C1), doi: 10.1029/2000JC000713.
Peter M. A. & Meylan M. H. 2004 Infinite-depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes. J. Fluid Mech. 500, 145167.
Peter M. A., Meylan M. H. & Chung H. 2004 Wave scattering by a circular elastic plate in water of finite depth: a closed form solution. Intl J. Offshore Polar Engng 14 (2), 8185.
Peter M. A., Meylan M. H. & Linton C. M. 2006 Water-wave scattering by a periodic array of arbitrary bodies. J. Fluid Mech. 548, 237256.
Porter R. & Evans D. V. 1999 Rayleigh-Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides. J. Fluid Mech. 386, 233258.
Porter R. & Evans D. V. 2005 Embedded Rayleigh-Bloch surface waves along periodic rectangular arrays. Wave Motion 43, 2950.
Thompson I. & Linton C. M. 2006 Resonant effects in scattering by periodic arrays. In Proc. 21st Intl Workshop on Water Waves and Floating Bodies, pp. 173176.
Twersky V. 1962 On scattering of waves by the infinite grating of circular cylinders. IRE Trans. Antennas and Propagation 10, 737765.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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