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A variational method for water wave radiation and diffraction problems

Published online by Cambridge University Press:  26 April 2006

J. A. P. Aranha and
C. P. Pesce
J. A. P. Aranha
Affiliation:
Department of Naval Engineering, USP, CP 61548, São Paulo, Brazil
C. P. Pesce
Affiliation:
Division of Naval and Oceânica Engineering, IPT, CP 7141, São Paulo, Brazil
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Abstract

It is shown that the linear and nonlinear exciting force coefficients, the added mass and radiation damping matrices, and the far-field wave amplitude (reflection and transmission coefficients in the two-dimensional case) can all be written as stationary values of well-defined functionals. As a consequence these quantities can be accurately determined with relatively crude approximations for the diffraction and radiation potentials. Numerical experiments confirm this feature: by inverting a 4 × 4 real symmetric matrix the results obtained by Vugts (1968), who computed the added mass and radiation damping matrices for several different geometries, were recovered over the whole range of frequencies.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989, pp. 135 - 157
Copyright
© 1989 Cambridge University Press

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