Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-01T10:28:02.467Z Has data issue: false hasContentIssue false

Measurement of high frequency capillary waves on steep gravity waves

Published online by Cambridge University Press:  12 April 2006

John H. Chang
Affiliation:
Department of Fluid Mechanics, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Richard N. Wagner
Affiliation:
Department of Fluid Mechanics, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Henry C. Yuen
Affiliation:
Department of Fluid Mechanics, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278

Abstract

The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

Type
Research Article
Copyright
© 1978 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

Benjamin, T. B. 1967 Instability of periodic wavetrains in nonlinear dispersive systems. Proc. Roy. Soc. A 299, 5975.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. I. Theory. J. Fluid Mech. 27, 417430.Google Scholar
Benney, D. J. 1976 Significant interactions between small and large scale surface waves. Studies in Appl. Math. 55, 95.Google Scholar
Cox, C. S. 1958 Measurement of slopes of high-frequency wind waves. J. Mar. Res. 16, 199225.Google Scholar
Crapper, G. D. 1970 Nonlinear capillary waves generated by steep gravity waves. J. Fluid Mech. 40, 149159.Google Scholar
Davies, T. V. 1951 The theory of symmetric gravity waves of finite amplitude. I. Proc. Roy. Soc. A 208, 475486.Google Scholar
Ferguson, W. E., Saffman, P. G. & Yuen, H. C. 1978 A model equation to study the effects of nonlinearity, surface tension and viscosity in water waves. Studies in Appl. Math. 85 (to appear).Google Scholar
Kinsman, B. 1965 Wind-Waves, Their Generation and Propagation on the Ocean Surface. Prentice-Hall.
Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a nonlinear continuous wave train. J. Fluid Mech. 83, 4975.Google Scholar
Longuet-Higgins, M. S. 1963 The generation of capillary waves by steep gravity waves. J. Fluid Mech. 16, 138159.Google Scholar
Mcgoldrick, L. F. 1972 On the rippling of small waves: a harmonic nonlinear nearly resonant interaction. J. Fluid Mech. 52, 725751.Google Scholar
Michell, J. H. 1893 The highest waves in water. Phil. Mag. Ser. (5), 36, 430437.Google Scholar
Miller, R. L. 1972 The role of surface tension in breaking waves. Tech. Rep. Univ. Chicago, no. 13. 1 October.Google Scholar
Stokes, G. G. 1880 Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Mathematical and Physical Papers, vol. 1, pp. 225238. Cambridge University Press.
Wilton, J. R. 1915 On ripples. Phil. Mag. 29, 688700.Google Scholar