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

  • F. A. Milinazzo (a1) (a2) and P. G. Saffman (a1)

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.

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Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647656 (referred to herein as BP).

Broadbent, E. G. & Moore, D. W.1985Waves of extreme form on a layer of uniform vorticity. Phys. Fluids28, 15611563.

Chen, B. & Saffman, P. G.1980Steady gravity—capillary waves on deep water. II Numerical results for finite amplitude. Stud. Appl. Maths62, 95111.

Dalrymple, R. A.1974A finite amplitude wave on a linear shear current. J. Geophys. Res.79, 44984504.

Moore, D. W. & Saffman, P. G.1982Finite amplitude waves in inviscid shear flow.. Proc. R. Soc. Lond. A382, 389410.

Okamura, M. & Oikawa, M.1989The linear stability of finite amplitude surface waves on a linear shearing flow. J. Phys. Soc. Japan58, 23862396.

Saffman, P. G. & Yuen, H. C. 1982 Finite-amplitude interfacial waves in the presence of a current. J. Fluid Mech. 123, 459476.

Simmen, J. A. & Saffman, P. G.1985Steady deep water waves on a linear shear current. Stud. Appl. Maths73, 3557.

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, 281302.

Zufiria, J. A. 1987 Non-symmetric gravity waves on water of infinite depth. J. Fluid Mech. 181, 1739.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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