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A note on solitary waves with variable surface tension in water of infinite depth

Published online by Cambridge University Press:  17 February 2009

E. Özuğurlu
Affiliation:
Bahcesehir University, Faculty of Arts and Sciences, Department of Mathematics and Computer Sciences, 34100 Besiktas, Istanbul, Turkey; e-mail: [email protected].
J.-M. Vanden-Broeck
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, England, UK.
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Abstract

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Two-dimensional gravity-capillary solitary waves propagating at the surface of a fluid of infinite depth are considered. The effects of gravity and of variable surface tension are included in the free-surface boundary condition. The numerical results extend the constant surface tension results of Vanden-Broeck and Dias to situations where the surface tension varies along the free surface.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Chen, B. and Saffman, P. G., “Steady gravity-capillary waves on deep water. II. Numerical results for finite amplitude”, Stud. Appl. Math. 62 (1980) 95111.CrossRefGoogle Scholar
[2]Dias, F. and Khariff, C., “Nonlinear gravity and capillary-gravity waves”, Ann. Rev. Fluid Mech. 31 (1999) 301346.Google Scholar
[3]Dias, F., Menasce, D. and Vanden-Broeck, J.-M., “Numerical study of capillary-gravity solitary waves”, Eur. J. Mech. B Fluids 15 (1996) 1736.Google Scholar
[4]Hogan, S. J., “Some effects of surface tension on steep water waves. Part 3”, J. Fluid Mech. 110 (1981) 381–10.Google Scholar
[5]Lucassen-Reynders, E. H. and Lucassen, J., “Properties of capillary waves”, Adv. Colloid Interface Sci. 2 (1969) 347395.Google Scholar
[6]Özuğurlu, E. and Vanden-Broeck, J.-M., “The influence of variable surface tension on capillary-gravity waves”, J. Eng. Math. 40 (2001) 269282.Google Scholar
[7]Schwartz, L. W. and Vanden-Broeck, J.-M., “Numerical solution of the exact equations for capillary-gravity waves”, J. Fluid Mech. 95 (1979) 119139.Google Scholar
[8]Vanden-Broeck, J.-M., “Capillary waves with variable surface tension”, Z. Angew. Math. Phys. 47 (1996) 799808.Google Scholar
[9]Vanden-Broeck, J.-M. and Dias, F., “Gravity-capillary solitary waves in water of infinite depth and related free-surface flows”, J. Fluid Mech. 240 (1992) 549557.Google Scholar