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On the virtual-mass and damping coefficients for long waves in water of finite depth

Published online by Cambridge University Press:  11 April 2006

F. Ursell
F. Ursell
Affiliation:
Department of Mathematics, University of Manchester, England
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Abstract

A half-immersed circular cylinder is making vertical oscillations on water of finite constant depth. The virtual-mass and damping coefficients are studied in the limit as the wavelength tends to infinity. It is found that the virtual-mass coefficient tends to a finite limit and that the amplitude ratio ultimately varies as the frequency. This behaviour differs from the behaviour for infinite depth, where the virtual-mass coefficient tends to infinity and the amplitude ratio ultimately varies as (frequency).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 1 , 14 July 1976 , pp. 17 - 28
Copyright
© 1976 Cambridge University Press

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References

Erdélyi, A. (ed.) 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.Google Scholar
Rhodes-Robinson, P. F. 1970 On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. Part II. Proc. Camb. Phil. Soc. 67, 443–468.Google Scholar
Ursell, F. 1949 On the heaving motion of a circular cylinder on the surface of a fluid. Quart. J. Mech. Appl. Math. 2, 218–231.Google Scholar
Yu, Y. S. & Ursell, F. 1961 Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment. J. Fluid Mech. 11, 529–551.Google Scholar