Abstract
Gravity capillary waves traveling at a constant velocity in water of finite depth are considered. The flow is assumed to be rotat ional and characterised by a constant vorticity. A general formulation of the problem as a system of integro differential equations is presented. This system is solved numerically and new results for steep waves are presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lamb, H. (1945) Hydrodynamics, Dover Publications, New York.
Vanden-Broeck, J.-M. and Dias, F. (1992) Solitary waves in water of infinite depth and related free surface flows, J. Fluid Mech. 240, 549–557.
Chen, B. and Saffman, P.G., 1979 Steady gravity-capillary waves on deep water. Stud. Appl. Math. 60, 183–210.
Crapper, G.D., 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 532–540.
Hogan, S.J., 1979 Some effects of surface tension on steep water waves. J. Fluid Meek. 91, 167–180.
Hunter, J.K. and Vanden-Broeck, J.-M., 1983 Solitary and periodic gravity-capillary waves of finite amplitude. J. Fluid Mech. 134, 205–219.
Kang, Y. and Vanden-Broeck, J.-M., 2000 Gravity-capillary waves in the presence of constant vorticity. Eur. J. Mech. B-Fluids 19, 253–268.
Kinnersley, W. 1976 Exact large amplitude capillary waves on sheets of fluid. J. Fluid Mech. 77, 229–241.
Longuet-Higgins, M.S. 1975 Integral properties of periodic gravity waves of finite amplitude Proc. Roy. Soc. Ser. A 342, 157–174.
Pullin, D.I. and Grimshaw, R.H.J. 1988 Finite amplitude solitary waves at the interface between two homogeneous fluids Phys. Fluids 31, 3550–3559.
Schwartz, L.W. 1974 Computer extension and analytic continuation of Stokes' expansion for gravity waves J. Fluid Mech. 62, 553–578.
Schwartz, L.W. and Vanden-Broeck, J.-M. 1979 Numerical solution of the exact equations for capillary-gravity waves J. Fluid Mech. 95, 119–139.
Simmen, J.A. and Saffman, P.G. 1985 Steady deep water waves on a linear shear current Stud. Appl. Math. 73, 35–57.
Stokes, G.G. 1847 On the theory of oscillatory waves Camb. Trans. 8, 441–473.
Teles Da Silva, A.F. and Peregrine, D.H. 1978 Steep surface waves on water of finite depth with constant vorticity J. Fluid Mech. 195, 281–302.
Vanden-Broeck, J.-M. 1991 Elevation solitary waves with surface tension Phys. Fluids bf A3, 2659–2663.
Vanden-Broeck, J.-M. 1994 Steep solitary waves in water of finite with constant vorticity J. Fluid Mech. 274, 339–348.
Vanden-Broeck, J.-M. 1995 New families of steep solitary in water of finite depth with constant vorticity Eur. J. Mech. B/Fluids 14, 761–774.
Vanden-Broeck, J.-M. 1996 Periodic waves with constant vorticity in water of infinite depth IMA J. Appl. Math. 56 207–217.
Vanden-Broeck, J.-M. and Dias F. 1992 Gravity-capillary solitary waves in water of infinite depth and related free-surface flows J. Fluid Mech. 240, 549–557.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Vanden-Broeck, JM., Kang, Y. (2001). Waves With Constant Vorticity. In: King, A.C., Shikhmurzaev, Y.D. (eds) IUTAM Symposium on Free Surface Flows. Fluid Mechanics and Its Applications, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0796-2_39
Download citation
DOI: https://doi.org/10.1007/978-94-010-0796-2_39
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3854-6
Online ISBN: 978-94-010-0796-2
eBook Packages: Springer Book Archive