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Existence and some properties of waves trapped by submerged cylinders

Published online by Cambridge University Press:  21 April 2006

J. A. P. Aranha
J. A. P. Aranha
Affiliation:
DINAV, I.P.T., São Paulo, Brazil
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Abstract

In this paper the mathematical formulation associated with waves trapped by submerged cylinders is recast as a standard eigenvalue problem. In this way the existence is proven of trapped waves for every frequency Ω, and for arbitrary geometry of the submerged cylinder. At the same time a simple expression for the first eigenvalue and eigenmode, correct in the limits Ω → 0 or Ω → ∞, is derived. The expression can be a useful approximation for a structure relatively transparent to the wave action such as, for instance, a semisubmersible platform.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 421 - 433
Copyright
© 1988 Cambridge University Press

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References

Abramowitz, M. & Stegun I. A. 1964 Handbook of Mathematical Functions. Dover.
Achenbach J. D. 1975 Wave Propagation in Elastic Solids. North-Holland.
Aranha J. A. P. 1988 Excitation of waves trapped by submerged slender structures, and nonlinear resonance. J. Fluid Mech. 192, 435–453.Google Scholar
Courant, R. & Hilbert D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.
Jones D. S. 1953 The eigenvalues of2 + = 0 when the boundary conditions are given in semi-infinite domains. Proc. Camb. Phil. Soc. 49, 668–684.Google Scholar
Ladyzhenskaya, O. & Ural'tseva N. 1968 Linear and Quasi-linear Elliptic Equations. Academic.
Longuet-Higgins M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.Google Scholar
McIver, P. & Evans D. V. 1985 The trapping of surface waves above a submerged horizontal cylinders. J. Fluid Mech. 151, 243–255.Google Scholar
Pinkster, J. A. & Huijsmans R. H. M. 1982 The low frequency motion of a semi-submersible in waves, Boss Conference, vol. 1 (ed. C. Chryssostomidis & J. J. Connor), pp. 447–466. Hemisphere.
Sobolev S. L. 1963 Application of Functional Analysis in Mathematical Physics. American Mathematical Society.
Stokes G. G. 1846 Report on recent researches in hydrodynamics. Brit. Assoc. Rep.Google Scholar
Ursell F. 1951 Trapping modes in the theory of surface waves. Proc. Camb. Phil. Soc. 47, 347–358.Google Scholar
Ursell F. 1952 Edge waves on sloping beach Proc. R. Soc. Lond. A 124, 79–97.Google Scholar
Ursell F. 1987 Mathematical aspects of trapping modes in the theory of surface waves. To appear.