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Surface-wave damping in a circular cylinder with a fixed contact line

Published online by Cambridge University Press:  26 April 2006

D. M. Henderson  and
J. W. Miles
D. M. Henderson
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
J. W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093–0225, USA
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Abstract

The natural frequencies and damping ratios for surface waves in a circular cylinder are calculated on the assumptions of a fixed contact line, Stokes boundary layers, and either a clean or a fully contaminated surface. These theoretical predictions are compared with the measurements for the first six modes in a brimfull, sharp-edged cylinder of radius 2.77 cm and depth 3.80 cm. The differences between the predicted and observed frequencies were less than 0.5% for all but the fundamental axisymmetric mode with a clean surface. The difference between the predicted and observed damping ratio for the dominant mode with a clean surface was 20%; this difference was significantly larger for the higher modes with a clean surface and for all of the modes with a contaminated surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 285 - 299
Copyright
© 1994 Cambridge University Press

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References

Ablett, R. 1923 An investigation of the angle of contact between paraffin wax and water. Phil. Mag. 46, 244–256.Google Scholar
Benjamin, T. B. & Scott, J. C. 1979 Gravity–capillary waves with edge constraints. J. Fluid Mech. 92, 241–267.Google Scholar
Case, K. M. & Parkinson, W. C. 1957 Damping of surface waves in an incompressible liquid. J. Fluid Mech. 2, 172–184.Google Scholar
Dore, B. D. 1978 Some effects of the air–water interface on gravity waves. Geophys. Astrophys. Fluid Dyn. 10, 215–230.Google Scholar
Graham-Eagle, J. 1983 A new method for calculating eigenvalues with applications to gravity–capillary waves with edge constraints. Math. Proc. Camb. Phil. Soc. 94, 553–564.Google Scholar
Henderson, D. M., Hammack, J., Kumar, P. & Shah, D. 1992 The effects of static contact angles on standing waves. Phys. Fluids A 4, 2320–2322.Google Scholar
Henderson, D. M. & Miles, J. W. 1991 Faraday waves in 2:1 internal resonance. J. Fluid Mech. 222, 429–470.Google Scholar
Hocking, L. M. 1987 The damping of capillary gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–256.Google Scholar
Kitchener, J. A. & Cooper, C. F. 1959 Current concepts in the theory of foaming. Q. Rev. Chem. Soc. 13, 71–97.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–473.Google Scholar
Miles, J. 1991a The capillary boundary layer for standing waves. J. Fluid Mech. 222, 197–205.Google Scholar
Miles, J. 1991b A note on surface films and surface waves. Wave Motion 13, 303–306.Google Scholar
Scott, J. C. 1977 The historical development of wave-calming using oil. Rep. 81. Fluid Mechanics Research Institute, University of Essex.
Scott, J. C. 1979 The preparation of clean water surfaces for fluid mechanics. In Surface Contamination: Genesis, Detection and Control, vol. 1 (ed. K. L. Mittal), pp. 477–497. Plenum.
Stokes, C. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106 (also Mathematical and Physical Papers, vol. 3, pp. 1–141, Cambridge University Press, 1922).Google Scholar