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Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions

Published online by Cambridge University Press:  21 April 2006

P. A. Martin  and
Robert A. Dalrymple
P. A. Martin
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK
Robert A. Dalrymple
Affiliation:
Ocean Engineering Group, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
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Abstract

The method of matched asymptotic expansions is applied to several long-wave problems including the scattering of acoustic waves by a grating of cylinders and the scattering of water waves incident on horizontal cylinders. It is shown that a naïve application of the method can lead to incorrect results. A modified expansion procedure is developed and applied to a number of problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 465 - 490
Copyright
© 1988 Cambridge University Press

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References

Burke, J. E. & Twersky, V. 1966 On scattering of waves by the infinite grating of elliptic cylinders. IEEE Trans. Antennas Propag. AP-14, 465–180.Google Scholar
Flagg, C. N. & Newman, J. N. 1971 Sway added-mass coefficients for rectangular profiles in shallow water. J. Ship Res. 15, 257–265.Google Scholar
Guiney, D. C., Noye, B. J. & Tuck, E. O. 1972 Transmission of water waves through small apertures. J. Fluid Mech. 55, 149–161.Google Scholar
Hayashi, T., Kano, T. & Shirai, M. 1966 Hydraulic research on the closely spaced pile breakwater. In Proc. 10th Coastal Engineering Conf., pp. 873–884. ASCE.
Kakuno, S. 1983 Reflection and transmission of waves through vertical slit-type structures. In Proc. Coastal Structures '83, pp. 939–952. ASCE, Arlington.
Kirby, J. T. & Dalrymple, R. A. 1983 Propagation of obliquely incident water waves over a trench. J. Fluid Mech. 133, 47–63.Google Scholar
Kreisel, G. 1949 Surface waves. Q. Appl. Maths 7, 21–44.Google Scholar
Lamb, H. 1898 On the reflection and transmission of electric waves by a metallic grating. Proc. Lond. Math. Soc. (1) 29, 523–544.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lamb, H. & Cook, G. 1910 A hydrodynamical illustration of the theory of the transmission of aerial and electrical waves by a grating. Phil. Mag. (6) 20, 303–309.Google Scholar
Lewin, L. 1951 Advanced Theory of Waveguides. Iliffe.
Lewin, L. 1975 Theory of Waveguides. Halstead.
Marcuvitz, N. (ed.) 1951 Waveguide Handbook. McGraw-Hill.
Martin, P. A. 1985 On the T-matrix for water-wave scattering problems. Wave Motion 7, 177–193.Google Scholar
Mei, C. C. & Black, J. L. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Miles, J. W. 1982a On Rayleigh scattering by a grating. Wave Motion 4, 285–292.Google Scholar
Miles, J. W. 1982b On surface-wave diffraction by a trench. J. Fluid Mech. 115, 315–325.Google Scholar
Miles, J. W. 1983 Surface-wave diffraction by a periodic row of submerged ducts. J. Fluid Mech. 128, 155–180.Google Scholar
Naftzger, R. A. & Chakrabarti, S. K. 1979 Scattering of waves by two-dimensional circular obstacles in finite water depths. J. Ship Res. 23, 32–42.Google Scholar
Newman, J. N. 1969 Lateral motion of a slender body between two parallel walls. J. Fluid Mech. 39, 97–115.Google Scholar
Newman, J. N. 1977 The interaction of stationary vessels with regular waves. In Proc. 11th Symp. on Naval Hydrodynamics, pp. 491–501. London, I. Mech. E.
Packham, B. A. & Williams, W. E. 1972 A note on the transmission of water waves through small apertures. J. Inst. Maths. Applies. 10, 176–184.Google Scholar
Richmond, H. W. 1923 On the electrostatic field of a plane or circular grating formed of thick rounded bars. Proc. Lond. Math. Soc. (2) 22, 389–403.Google Scholar
Sedov, L. I. 1965. Two-dimensional Problems in Hydrodynamics and Aerodynamics. Interscience.
Smythe, W. R. 1968 Static and Dynamic Electricity, 3rd edn. McGraw-Hill.
Spring, B. H. & Monkmeyer, P. L. 1975 Interaction of plane waves with a row of cylinders. Proc. Civil Engineering in the Oceans, III, pp. 979–998. ASCE, Newark, Delaware.
Stoker, J. J. 1957 Water Waves. Interscience.
Taylor, P. J. 1973 The blockage coefficient for flow about an arbitrary body immersed in a channel. J. Ship Res. 17, 97–105.Google Scholar
Tuck, E. O. 1975 Matching problems involving flow through small holes. Adv. Appl. Mech. 15, 89–158.Google Scholar
Tuck, E. O. 1977 Some classical water-wave problems in varying depth. Waves on Water of Variable Depth, Lecture Notes in Physics vol. 64, pp. 9–20. Springer.
Twersky, V. 1956 On the scattering of waves by an infinite grating. IRE Trans. Antennas Propag. 4, 330–345.Google Scholar
Twersky, V. 1961 Elementary function representations of Schlömilch series. Arch. Rat. Mech. Anal. 8, 323–332.Google Scholar
Twersky, V. 1962 On scattering of waves by the infinite grating of circular cylinders. IRE Trans. Antennas Propag. 10, 737–765.Google Scholar
Ursell, F. 1976 On the virtual-mass and damping coefficients for long waves in water of finite depth. J. Fluid Mech. 76, 17–28.Google Scholar
Ursell, F. 1981 Irregular frequencies and the motion of floating bodies. J. Fluid Mech. 105, 143–156.Google Scholar