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The interaction of waves with a row of circular cylinders

Published online by Cambridge University Press:  26 April 2006

C. M. Linton  and
D. V. Evans
C. M. Linton
Affiliation:
University of Bristol, University Walk, Bristol BS8 1TW, UK
D. V. Evans
Affiliation:
University of Bristol, University Walk, Bristol BS8 1TW, UK
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Abstract

The two-dimensional acoustics problem of the scattering of an obliquely incident plane wave by a row of equally-spaced circular cylinders is solved using multipole expansions. The method is superior to existing techniques available for this problem as it allows the far-field behaviour of the solution to be evaluated in a straightforward manner, and extensive results for the reflection and transmission coefficients are given. The problem described above has a direct analogue in the theory of water waves and this is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 687 - 708
Copyright
© 1993 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.
Achenbach, J. D., Lu, Y.-C. & Kitahara, M. 1988 3-D reflection and transmission of sound by an array of rods. J. Sound. Vib. 125, (3), 463–476.Google Scholar
Callan, M., Linton, C. M. & Evans, D. V. 1991 Trapped modes in two-dimensional waveguides. J. Fluid Mech. 229, 51–64.Google Scholar
Ignatowsky, W. von 1914 Zur Theorie der Gitter. Annln Phys. 44.
Jones, D. S. 1986 Acoustic and Electromagnetic Waves. Clarendon.
Lamb, H. 1945 Hydrodynamics. Dover.
Linton, C. M. & Evans, D. V. 1990 The interaction of waves with arrays of vertical circular cylinders. J. Fluid Mech. 215, 549–569.Google Scholar
Linton, C. M. & Evans, D. V. 1992 The radiation and scattering of surface waves by a vertical circular cylinder in a channel. Phil. Trans. R. Soc. Lond. A 338, 325–357.Google Scholar
MacCamy, R. C. & Fuchs, R. A. 1954 Wave forces on piles: A diffraction theory. US Army Coastal Engineering Research Center, Tech. Mem. 69.Google Scholar
Macfarlane, G. G. 1946 Surface impedance of an infinite parallel-wire grid at oblique angles of incidence. J. IEEE 93, (IIIA), 1523–1527.Google Scholar
McIver, P. & Bennett, G. S. 1992 Scattering of water waves by axisymmetric bodies in a channel J. Engng Maths 27, 1–29.Google Scholar
Martin, P. A. & Dalrymple, R. A. 1988 Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions. J. Fluid Mech. 188, 465–490.Google Scholar
Miles, J. W. 1982 On Rayleigh scattering by a grating. Wave Motion 4, 285–292.Google Scholar
Miles, J. W. 1983 Surface-wave diffraction by a periodic row of submerged ducts. J. Fluid Mech. 128, 155–180.Google Scholar
Petit, R. 1980 Electromagnetic Theory of Gratings. Topics in Current Physics, vol. 22. Springer.
Spring, B. H. & Monkmeyer, P. L. 1974 Interaction of plane waves with vertical cylinders. InProc. 14th Intl. Conf. on Coastal Engng, chap. 107, 1828–1845.
Spring, B. H. & Monkmeyer, P. L. 1975 Interaction of plane waves with a row of cylinders. InProc. 3rd Conf. on Civil Engng in Oceans, ASCE, Newark, Delaware, 979–998.
Thomas, G. P. 1991 The diffraction of water waves by a circular cylinder in a channel. Ocean Engng 18 (1/2), 17–44.Google Scholar
Thorne, R. C. 1953 Multipole expansions in the theory of surface waves. Proc. Camb. Phil. Soc. 49, 707–716.Google Scholar
Twersky, V. 1956 On the scattering of waves by an infinite grating. IRE Trans. on Antennas and Propagation 4, 330–345.Google Scholar
Twersky, V. 1962 On scattering of waves by the infinite grating of circular cylinders. IRE Trans. on Antennas and Propagation 10, 737–765.Google Scholar
Wilcox, C. H. 1984 Scattering Theory for Diffraction Gratings. Springer.
Yeung, R. W. & Sphaier, S. H. 1989 Wave-interference effects on a truncated cylinder in a channel. J. Eng Maths 23, 95–117.Google Scholar
Závik, F. 1913 Über die Beugung Elektromagnetischer Wellen an parallelen, unendlich langen Kreiszylindern. Annln Phys. 40, 1023–1056.Google Scholar