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A note on variational principles for surface-wave scattering

Published online by Cambridge University Press:  29 March 2006

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

Complementary variational formulations are developed for the scattering of a gravity wave by a circular dock. These formulations, which are based on assumed distributions of the radial velocity and the potential, respectively, on the projection of the cylindrical boundary, yield lower and upper bounds to an impedance parameter that determines the difference between the scattered wave for the dock and the corresponding wave for a circular cylinder. Numerical results, using trial functions based on the incident wave, are compared with the results implied by a Galerkin solution (Garrett 1971). The maximum errors in the variational approximations to the total scattering cross-section are found to be of the order of 2% for a typical depth/radius ratio, draft/depth ratios of 0, ½ and 1, and all wavelengths. The axisymmetric component of the scattering cross-section is found to be very close to the value for scattering by a circular cylinder (dock extending to bottom). The intensity of the scattered wave on the forward axis for long wavelengths and a certain range of the geometric parameters is significantly less than that for a circular cylinder, and may vanish for critical combinations of these parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 1 , 15 March 1971 , pp. 141 - 149
Copyright
© 1971 Cambridge University Press

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References

Garrett, C. J. R. 1971 Wave forces on a circular dock J. Fluid Mech. 46, 129.Google Scholar
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Miles, J. W. & Gilbert, J. F. 1968 Scattering of gravity waves by a circular dock J. Fluid Mech. 34, 783–93.Google Scholar