Wavenumber Spectrum of Very Short Wind Waves: An Application of Two-Dimensional Slepian Windows to Spectral Estimation

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  • 1 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

A multitaper 2D spectral estimation method is developed for increasing the degree of freedom of the estimation. The core of this method is 2D Slepian eigen windows that are optimum in the sense of minimizing the spectral leakage. Wavenumber spectra of very short wind wave slopes are calculated by this method. The advantages of the multitaper technique are shown by obtaining smooth wavenumber spectra from a limited amount of image data. The data used for the spectral estimation were measured in the laboratory with a water surface gradient detector developed by the authors. Important features of the spatial distribution of short-wave energy are newly revealed. The widening of angular spreading of energy density spectra is not monotonic with increasing wave-number. There is a local plat region of minimum angular spreading in the spectral band of parasitic capillary waves that suggests that there is another upstream of energy cascade in spite of the energetic gravity-wave spectral peak. The input energy of parasitic waves from energetic long gravity waves with a narrow angular distribution is dominant over energy cascade down from spectrally close short waves with a broad angular distribution. The omnidirectional energy spectra also show features related to the change of energy spreading. There is a local wave energy maximum of parasitic waves and a local wave energy minimum of gravity–capillary waves.

Abstract

A multitaper 2D spectral estimation method is developed for increasing the degree of freedom of the estimation. The core of this method is 2D Slepian eigen windows that are optimum in the sense of minimizing the spectral leakage. Wavenumber spectra of very short wind wave slopes are calculated by this method. The advantages of the multitaper technique are shown by obtaining smooth wavenumber spectra from a limited amount of image data. The data used for the spectral estimation were measured in the laboratory with a water surface gradient detector developed by the authors. Important features of the spatial distribution of short-wave energy are newly revealed. The widening of angular spreading of energy density spectra is not monotonic with increasing wave-number. There is a local plat region of minimum angular spreading in the spectral band of parasitic capillary waves that suggests that there is another upstream of energy cascade in spite of the energetic gravity-wave spectral peak. The input energy of parasitic waves from energetic long gravity waves with a narrow angular distribution is dominant over energy cascade down from spectrally close short waves with a broad angular distribution. The omnidirectional energy spectra also show features related to the change of energy spreading. There is a local wave energy maximum of parasitic waves and a local wave energy minimum of gravity–capillary waves.

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