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On the incipient breaking of small scale waves

Published online by Cambridge University Press:  29 March 2006

M. L. Banner  and
O. M. Phillips
M. L. Banner
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
O. M. Phillips
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
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Abstract

It is shown that the surface wind drift in the ocean substantially reduces the maximum wave height ξx and wave orbital velocity that can be attained before breaking. If q is the magnitude of the surface drift at the point where the wave profile crosses the mean water level and c is the wave speed, then \[ \zeta_{\max} = \frac{c^2}{2g}\bigg(1-\frac{q}{c}\bigg)^2. \] Incipient breaking in a steady wave train is characterized by the occurrence of stagnation points at wave crests, but not necessarily by discontinuities in slope. After breaking, there is in the mean flow a stagnation point relative to the wave profile near the crest of the broken wave, on one side of which the water tumbles forward and behind which it recedes more smoothly to the rear. Some simple flow visualization studies indicate the general extent of the wake behind the breaking region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 4 , 2 October 1974 , pp. 647 - 656
Copyright
© 1974 Cambridge University Press

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References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory J. Fluid Mech. 27, 417.Google Scholar
Longuet-Higgins, M. S. 1960 Mass transport in the boundary layer at a free oscillating surface J. Fluid Mech. 8, 293.Google Scholar
Longuet-Higgins, M. S. 1973 A model of flow separation at a free surface. J. Fluid Mech. 57, 129.Google Scholar
Lamb, H. 1953 Hydrodynamics. Cambridge University Press.
Michell, A. G. M. 1893 The highest waves in water. Phil. Mag. 36 (5), 430.Google Scholar
Stokes, G. G. 1880 On the theory of oscillatory waves. Papers, pp. 1, 197, 227. Cambridge University Press.
Wu, J. 1968 Laboratory studies of wind–wave interactions J. Fluid Mech. 34, 91.Google Scholar