TECHNICAL PAPERS
May 1, 2006

Wave Forcing of Small Floating Bodies

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132, Issue 3

Abstract

We investigate the drift of small bodies (bodies which do not significantly disturb the fluid) in waves. We begin with the slope sliding models of Rumer and Marchenko, and we establish that the models are different and that the correct model is due to Marchenko. We then investigate the slope sliding model when we have linear wave forcing of constant frequency (for which the differences between the two models vanish). We establish that the drift velocity, for this case, is independent of initial position, which contradicts published results in which drift velocity was shown to depend on initial position. The reason for the error in previous results was the slow decay of the transient motion. For this reason we present a numerical method to calculate the drift velocity, which avoids the problems associated with the slow decay of the transient motion. Some results for the drift velocity are given.

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References

Hildebrand, F. B. (1965). Methods of applied mathematics, 2nd Ed., Prentice–Hall, Englewood Cliffs, N.J.
Marchenko, A. V. (1999). “The floating behaviour of a small body acted upon by a surface wave.” J. Appl. Math. Mech., 63(3), 471–478.
Perko, L. P. (1991). Differential equations and dynamical systems, Springer, New York.
Rumer, R. R., Crisman, R., and Wake, A. (1979). “Ice transport in great lakes.” Water Resources and Environmental Engineering Research Rep. No. 79-3, NY State Univ. at Buffalo, Buffalo, N.Y.
Shen, H. H., and Ackley, A. F. (1991). “A one-dimensional model for wave inducted ice-flow collisions.” Ann. Glaciol., 15, 87–95.
Shen, H. H., and Zhong, Y. (2001). “Theoretical study of the drift of small rigid floating objects in a wave field.” J. Waterw., Port, Coastal, Ocean Eng., 127(6), 343–351.

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Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132Issue 3May 2006
Pages: 192 - 198

History

Received: Jul 7, 2004
Accepted: Jul 5, 2005
Published online: May 1, 2006
Published in print: May 2006

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Authors

Affiliations

Rike Grotmaack [email protected]
Institute of Information and Mathematical Sciences, Massey Univ., Auckland, New Zealand; presently, Zentrum für Technomathematik, Univ. of Bremen, Germany. E-mail: [email protected]
Michael H. Meylan [email protected]
Professor, Institute of Information and Mathematical Sciences, Massey Univ., Auckland, New Zealand. Current address: Department of Mathematics, Private Bag 92019, Univ.of Auckland, Auckland, New Zealand. E-mail: [email protected]

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