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On surface-wave forcing by a circular disk

Published online by Cambridge University Press:  21 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093, USA
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Abstract

The radiation resistance (damping coefficient) and virtual mass for a circular disk that executes small, heaving oscillations at the surface of a semi-infinite body of water, originally calculated by MacCamy (1961a) through the numerical solution of an integral equation, are calculated from a systematic hierarchy of variational approximations. The first member of this hierarchy is based on the exact solution of the boundary-value problem for α = 0 and is in error by less than 2% for 0 [les ] α [les ] 1, where α = aσ2/g (a = radius of disk, σ = angular frequency, g = gravity). The second approximation provides a variational interpolation between the limiting results for α = 0 and α = ∞ and appears to be in error by less than 2% for all α except in certain narrow intervals, where pseudoresonances pose difficulties. Those difficulties are overcome by local reference to the third approximation. Numerical results are plotted for 0 [les ] α [les ] 10. Asymptotic results for α ↑ ∞ are developed in an Appendix.

The corresponding formulation and the first variational approximation are developed for pitching oscillations of the disk.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 97 - 108
Copyright
© 1987 Cambridge University Press

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