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Capillary–gravity and capillary waves generated in a wind wave tank: observations and theories

Published online by Cambridge University Press:  26 April 2006

Xin Zhang
Xin Zhang
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0230, USA
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Abstract

Short water surface waves generated by wind in a water tunnel have been measured by an optical technique that provides a synoptic picture of the water surface gradient over an area of water surface (Zhang & Cox 1994). These images of the surface gradient can be integrated to recover the shape of the water surface and find the two-dimensional wavenumber spectrum. Waveforms and two-dimensional structures of short wind waves have many interesting features: short and steep waves featuring sharp troughs and flat crests are very commonly seen and most of the short waves are far less steep than the limiting wave forms; waveforms that resemble capillary–gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989); capillaries are mainly found as parasitics on the downwind faces of gravity waves, and the longest wavelengths of those parasitic capillaries found are less than 1 cm; the phenomenon of capillary blockage (Phillips 1981) on dispersive freely travelling short waves is also observed. The spectra of short waves generated by low winds show a characteristic dip at the transition wavenumber between the gravity and capillary regimes, and the dip becomes filled in as the wind increases. The spectral cut-off at high wavenumbers shows a power law behaviour with an exponent of about minus four. The wavenumber of the transition from the dip to the cut-off is not sensitive to the change of wind speed. The minus fourth power law of the extreme capillary wind wave spectrum can be explained through a model of energy balances. The concept of an equilibrium spectrum is still useful. It is shown that the dip in the spectrum of capillary–gravity waves is a result of blockage of both capillary–gravity wind waves and parasitic capillary waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 51 - 82
Copyright
© 1995 Cambridge University Press

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