Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-09T05:55:05.850Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form

Published online by Cambridge University Press:  26 April 2006

F. A. Milinazzo  and
P. G. Saffman
F. A. Milinazzo
Affiliation:
Applied Mathematics 217-50, California Institute of Technology, Pasadena, CA 91125, USA Royal Roads Military College, Victoria, BC, Canada.
P. G. Saffman
Affiliation:
Applied Mathematics 217-50, California Institute of Technology, Pasadena, CA 91125, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Calculations are carried out of the shape of gravity and gravity–capillary waves on deep water in the presence of a thin sheet of uniform vorticity which models the effect of a wind drift layer. The dependence of the fluid speed at the wave crest is determined and compared for gravity waves with the theory of Banner & Phillips (1974). It is found that this theory underestimates the retardation due to drift and tendency to break. The retardation disappears when capillary forces are significant, but in this case it is found that there can be a significant alteration of the wave shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 93 - 101
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647–656 (referred to herein as BP).Google Scholar
Broadbent, E. G. & Moore, D. W. 1985 Waves of extreme form on a layer of uniform vorticity. Phys. Fluids 28, 1561–1563.Google Scholar
Chen, B. & Saffman, P. G. 1980 Steady gravity—capillary waves on deep water. II Numerical results for finite amplitude. Stud. Appl. Maths 62, 95–111.Google Scholar
Dalrymple, R. A. 1974 A finite amplitude wave on a linear shear current. J. Geophys. Res. 79, 4498–4504.Google Scholar
Moore, D. W. & Saffman, P. G. 1982 Finite amplitude waves in inviscid shear flow.. Proc. R. Soc. Lond. A 382, 389–410.Google Scholar
Okamura, M. & Oikawa, M. 1989 The linear stability of finite amplitude surface waves on a linear shearing flow. J. Phys. Soc. Japan 58, 2386–2396.Google Scholar
Saffman, P. G. & Yuen, H. C. 1982 Finite-amplitude interfacial waves in the presence of a current. J. Fluid Mech. 123, 459–476.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 steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–302.Google Scholar
Zufiria, J. A. 1987 Non-symmetric gravity waves on water of infinite depth. J. Fluid Mech. 181, 17–39.Google Scholar