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Particle trajectories in nonlinear gravity–capillary waves

Published online by Cambridge University Press:  20 April 2006

S. J. Hogan
S. J. Hogan
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Permanent address: Mathematical Institute, University of Oxford, St Giles, Oxford OX1 3LB.
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Abstract

The trajectories of surface and subsurface particles of nonlinear gravity–capillary waves are calculated. Surface tension is found to have a small effect on the trajectories and drift velocity of pure gravity waves (down to 20 cm in length). On the other hand, pure capillary wave trajectories can be considerably altered even when the influence of gravity is small (waves of up to 2 cm in length). When the restoring forces are of comparable magnitude, some remarkable trajectories are possible, containing one or more subloops. Overall, the influence of increased surface tension is to increase the relative horizontal distance travelled by a particle, as well as the magnitude of the time-averaged drift velocity ratio at the surface and, as far as short waves are concerned, its penetration depth.

These results can have implications for steep waves where parasitic capillaries are generated and for observations of the wind-drift current.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 105 - 119
Copyright
© 1985 Cambridge University Press

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References

Chen, B. & Saffman P. G.1979 Steady gravity—capillary waves on deep water. I. Weakly nonlinear waves. Stud. Appl. Maths 60, 183–210.Google Scholar
Chen, B. & Saffman P. G.1980 Steady gravity—capillary waves on deep water. II. Numerical results for finite amplitude waves. Stud. Appl. Maths 62, 95–111.Google Scholar
Hogan S. J.1980 Some effects of surface tension on steep water waves. 2. J. Fluid Mech. 96, 417–445.Google Scholar
Hogan S. J.1981 Some effects of surface tension on steep water waves. 3. J. Fluid Mech. 110, 381–410.Google Scholar
Hogan S. J.1984 Particle trajectories in nonlinear capillary waves. J. Fluid Mech. 143, 243–252.Google Scholar
Lamb H.1932 Hydrodynamics, 6th edn. Cambridge University Press.
Longuet-Higgins M. S.1979 The trajectories of particles in steep, symmetric gravity waves. J. Fluid Mech. 94, 497–517.Google Scholar
Srokosz M. A.1981 A note on particle trajectories in the highest wave. J. Fluid Mech. 111, 491–495.Google Scholar
Wilton J. R.1915 On ripples Phil. Mag. (6) 29, 688–700.Google Scholar