Slope wavenumber spectrum models of capillary and capillary-gravity waves |
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Authors: | Yongjun Jia Jie Zhang Yanfeng Wang |
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Institution: | 1. Institute of Oceanology, Chinese Academy of Sciences, Qingdao, 266071, China 2. Graduate School, Chinese Academy of Sciences, Beijing, 100039, China 3. First Institute of Oceanography, State Oceanic Administration, Qingdao, 266061, China
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Abstract: | Capillary and capillary-gravity waves possess a random character, and the slope wavenumber spectra of them can be used to
represent mean distributions of wave energy with respect to spatial scale of variability. But simple and practical models
of the slope wavenumber spectra have not been put forward so far. In this article, we address the accurate definition of the
slope wavenumber spectra of water surface capillary and capillary-gravity waves. By combining the existing slope wavenumber
models and using the dispersion relation of water surface waves, we derive the slope wavenumber spectrum models of capillary
and capillary-gravity waves. Simultaneously, by using the slope wavenumber models, the dependence of the slope wavenumber
spectrum on wind speed is analyzed using data obtained in an experiment which was performed in a laboratory wind wave tank.
Generally speaking, the slope wavenumber spectra are influenced profoundly by the wind speed above water surface. The slope
wavenumber spectrum increases with wind speed obviously and do not cross each other for different wind speeds. But, for the
same wind speed, the slope wavenumber spectra are essentially identical, even though the capillary and capillary-gravity waves
are excited at different times and locations. Furthermore, the slope wavenumber spectra obtained from the models agree quite
well with experimental results as regards both the values and the shape of the curve. |
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