Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T11:51:29.691Z Has data issue: false hasContentIssue false

Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane-wave approximation

Published online by Cambridge University Press:  20 April 2006

M. J. Simon
Affiliation:
Department of Mathematics, The University, Manchester

Abstract

A technique is developed to model the multiple scattering of surface waves in an array of axisymmetric wave-energy devices. The matrix equation which results is inverted to yield the exciting forces, the added-damping and added-mass matrices, the optimal power absorption and the optimal device responses. The matrix method is also used on the previously unstudied problem of an unconstrained array. Finite-size effects of devices are shown to be important in producing phase-shifts, which shift the uncon- strained frequency response, but leave the opt,imal energy absorption virtually unchanged.

Type
Research Article
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. National Bureau of Standards.
Budal, K. 1977 Theory for absorption of wave power by a system of interacting bodies. J. Ship Res. 21, 248253.Google Scholar
Count, B. M. & Jefferys, E. R. 1980 Wave power: the primary interface. In Proc. 13th Symp. Naval hydrodynamics, Tokyo, pp. 817826.
Davis, A. M. J. 1976 A relation between the radiation and scattering of surface waves by axisymmetric bodies. J. Fluid Mech. 76, 8588.Google Scholar
Evans, D. V. 1980 Some theoretical aspects of three-dimensional wave-energy absorbers. In Proc. 1st Symp. Wave-Energy Utilisation, Gothenburg, 1979. Chalmers Tech. Univ.
Greenhow, M. J. L. 1980 The hydrodynamic interactions of spherical wave-power devices in surface waves. In Power from sea waves (ed. B. M. Count), pp. 287343. Academic.
Lighthill, M. J. 1979 Two-dimensional analyses related to wave-energy extraction by submerged resonant ducts. J. Fluid Mech. 91, 253317.Google Scholar
Ohkusu, M. 1973 Wave action on groups of vertical circular cylinders. In Selected Papers from J. Soc. Naval Architects of Japan, vol. 11, pp. 3750.
Ohkusu, M. 1974 Hydrodynamic forces on multiple cylinders in waves. In Proc. Int. Symp. Dynamics of Marine Vehicles and Structures in Waves, London paper no. 12, pp. 107112. Inst. Mech. Engrs.
Simon, M. J. 1981 Wave-energy extraction by a submerged cylindrical resonant duct. J. Fluid Mech. 104, 159187.Google Scholar
Srokosz, M. A. 1979a Some theoretical aspects of wave-power absorption. Ph.D. thesis. Univ. Bristol.
Srokosz, M. A. 1979b The submerged sphere as an absorber of wave power. J. Fluid Mech. 95, 717741.Google Scholar
Srokosz, M. A. & Evans, D. V. 1979 A theory for wave-power absorption by two independently oscillating bodies. J. Fluid Mech. 90, 337362.Google Scholar
Thomas, G. P. & Evans, D. V. 1981 Arrays of three-dimensional wave-energy absorbers. J. Fluid Mech. 108, 6788.Google Scholar