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Steep solitary waves in water of finite depth with constant vorticity

Published online by Cambridge University Press:  26 April 2006

J.-M. Vanden-Broeck
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics and Center for the Mathematical Sciences, University of Wisconsin-Madison, WI 53705, USA
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Abstract

Solitary waves with constant vorticity in water of finite depth are calculated numerically by a boundary integral equation method. Previous calculations are confirmed and extended. It is shown that there are branches of solutions which bifurcate from a uniform shear current. Some of these branches are characterized by a limiting configuration with a 120° angle at the crest of the wave. Other branches extend for arbitrary large values of the amplitude of the wave. The corresponding solutions ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. A numerical scheme is presented to calculate directly these closed regions of constant vorticity. In addition, it is shown that there are branches of solutions which do not bifurcate from a uniform shear flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 339 - 348
Copyright
© 1994 Cambridge University Press

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References

Benjamin, T. B. 1962 The solitary wave on a stream with an arbitrary distribution of vorticity. J. Fluid Mech. 12, 97–116.Google Scholar
Hunter, J. K. & Vanden-Broeck, J.-M. 1983 Accurate computations for steep solitary waves. J. Fluid Mech. 136, 63–71.Google Scholar
Pullin, D. I. & Grimshaw, R. H. J. 1988 Finite amplitude solitary waves at the interface between two homogeneous fluids. Phys. Fluids 31, 3550–3559.Google Scholar
Sha, H. & Vanden-Broeck, J.-M. 1993 Two layer flows past a semicircular obstruction. Phys. Fluids A 5, 2661–2668.Google Scholar
Shira, V. I. 1986 Nonlinear waves at the surface of a liquid layer with a constant vorticity. Dokl. Acad. Nauk. 286, 1332–1336.Google Scholar
Simmen, J. A. & Saffman, P. G. 1985 Steady deep water waves on a linear shear current. Stud. Appl. Maths 73, 35–57.Google Scholar
Teles da Silva, A. F., & Peregrine, D. H. 1988 Steep surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–302.Google Scholar
Vanden-Broeck, J.-M. 1991 Elevation solitary waves with surface tension. Phys. Fluids A 3, 2659–2663.Google Scholar
Vanden-Broeck, J.-M. & Dias, F. 1992 Gravity-capillary solitary waves in water of infinite depth and related free-surface flows. J. Fluid Mech. 240, 549–557.Google Scholar
Vanden-Broeck, J.-M. & Tuck, E. O. 1994 Steady inviscid rotational flows with free surfaces. J. Fluid Mech. 258, 105–113.Google Scholar