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Surface-wave diffraction by a periodic row of submerged ducts

Published online by Cambridge University Press:  20 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego
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Abstract

The diffraction of a gravity wave of length λ that is obliquely incident upon, and the radiation from, a periodic row of vertical circular ducts of radii a and horizontal spacing b with mouths at a distance h below the free surface of a deep ocean are determined through integral-equation and variational formulations. Numerical results for the reflection coefficient, the pressure-amplification factor (the ratio of the complex amplitude of the wave-induced pressure in the depths of the duct to that of the incident wave at the level of the mouths), and the radiation impedance (the real and imaginary parts of which are measures of the radiation damping and the virtual mass or stiffness of the fluid external to the ducts) are presented as functions of a/λ with a/b and a/h as parameters for the special case of normal incidence with λ > b (which implies that the crests of the scattered waves are parallel to the midplane of the ducts). These results, which complement those of Simon (1981) for a single duct, are of practical interest for wave-power absorption.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 128 , March 1983 , pp. 155 - 180
Copyright
© 1983 Cambridge University Press

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References

Evans, D. V. 1981 Power from water waves Ann. Rev. Fluid Mech. 13, 157–187.Google Scholar
Falnes, J. & Budal, K. 1982 Wave-power absorption by parallel rows of interacting bodies. Appl. Ocean Res. (to be published).Google Scholar
Havelock, T. H. 1929 Forced surface waves on water. Phil. Mag. 8(7), 569–576.Google Scholar
Knott, G. F. & Flower, J. O. 1980 Wave-tank experiments on an immersed vertical circular duct J. Fluid Mech. 100, 225–236.Google Scholar
Lighthill, J. 1979 Two-dimensional analyses related to wave-energy extraction by submerged resonant ducts J. Fluid Mech. 91, 253–317.Google Scholar
Magnus, W., Oberhettinger, F. & Soni, R. P. 1966 Formulas and Theorems for the Special Functions of Mathematical Physics. Springer.
Miles, J. W. 1982a On surface-wave radiation from a submerged cylindrical duct J. Fluid Mech. 122, 339–346.Google Scholar
Miles, J. W. 1982b Surface-wave interaction with a deeply submerged circular duct. J. Austral. Math. Soc. (to be published).Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Schwinger, J. S. & Saxon, D. S. 1968 Discontinuities in Waveguides, pp. 26, 27. Gordon & Breach.
Simon, M. J. 1981 Wave-energy extraction by a submerged cylindrical resonant duct J. Fluid Mech. 104, 159–187.Google Scholar
Simon, M. J. 1982 Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane-wave approximation J. Fluid Mech. 120, 1–25.Google Scholar
Srokosz, M. A. 1980 Some relations for bodies in a canal with reference to wave-power absorption J. Fluid Mech. 99, 145–162.Google Scholar
Thomas, J. R. 1981 The absorption of wave energy by a three-dimensional submerged duct J. Fluid Mech. 104, 189–215.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 IEEE Trans. on Antennas and Propagation 10, 737–765.Google Scholar
Watson, G. N. 1945 A Treatise on the Theory of Bessel Functions. Cambridge University Press.