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Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder

Published online by Cambridge University Press:  07 April 2010

R. M. MOREIRA  and
D. H. PEREGRINE
R. M. MOREIRA*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
D. H. PEREGRINE
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Present address: Computational Fluid Dynamics Laboratory, Fluminense Federal University, Rua Passo da Pátria 156, bl.D, sl.563A, Niterói, RJ 24210-240, Brazil. Email address for correspondence: roger@vm.uff.br.
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Abstract

A submerged cylinder in a uniform stream flow is approximated by a horizontal doublet, following Lamb's classical method. A linear steady solution including surface tension effects is derived, showing that under certain conditions small-scale ripples are formed ahead of the cylinder, while a train of ‘gravity-like’ waves appear downstream. Surface tension effects and a dipole are included in the fully nonlinear unsteady non-periodic boundary-integral solver described by Tanaka et al. (J. Fluid Mech., vol. 185, 1987, pp. 235–248). Nonlinear effects are modelled by considering a flat free surface or the linear stationary solution as an initial condition for the fully nonlinear irrotational flow programme. Long-run computations show that these unsteady flows approach a steady solution for some parameters after waves have radiated away. In other cases the flow does not approach a steady solution. Interesting features at the free surface such as the appearance of ‘parasitic capillaries’ near the crest of gravity waves and the formation of capillary–gravity waves upstream of the cylinder are found.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 485 - 507
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

‡

Professor Peregrine passed away before this paper was completed. This manuscript was prepared for publication by the first author.

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