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Equilibrium Spectra of Wind Waves

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  • 1 School of Mathematics, University of New South Wales, Kensington, N.S.W., Australia
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Abstract

Equilibrium spectral behavior for ocean gravity wind waves has been investigated actively over the past three decades, yet fundamental problems remain in reconciling theory with observations. Predicted equilibrium spectral forms from physical models proposed recently by Kitaigorodskii and by Phillips are examined in the light of wavenumber and frequency spectra reported by several investigators. While frequency domain observations appear to support the model predictions, observed wavenumber spectra are found to differ both in the spectral dependence on wavenumber and on the wind speed.

Based on observed wavenumber and frequency spectra for fetch-limited condition a model is proposed for the form of the directional wavenumber spectrum slice in the dominant wave direction. Reduced wavenumber and frequency spectra are calculated from this model, assuming an empirical spectral directional spreading function and the linear gravity wave dispersion relation. These calculations reveal the underlying influences which shape these reduced spectra. In the energy containing subrange, just above the spectral peak, the dominant influence shaping these spectra is the variation of the directional spreading function with distance from the spectral peak. For frequency spectra, at higher frequencies, the model calculations predict that the range of observed frequency spectral dependences is due primarily to the Doppler shifting from advection of the shorter waves by the orbital motion of the dominant waves, with possible additional influences of wind drift and ambient currents.

Combining these results, composite calculated frequency spectra and one-dimensional wavenumber spectra show close correspondence with measured field spectra. In addition to clarifying the key processes that shape different regimes in the frequency spectrum, a refinement of the bounds of the gravity equilibrium subrange is proposed.

Abstract

Equilibrium spectral behavior for ocean gravity wind waves has been investigated actively over the past three decades, yet fundamental problems remain in reconciling theory with observations. Predicted equilibrium spectral forms from physical models proposed recently by Kitaigorodskii and by Phillips are examined in the light of wavenumber and frequency spectra reported by several investigators. While frequency domain observations appear to support the model predictions, observed wavenumber spectra are found to differ both in the spectral dependence on wavenumber and on the wind speed.

Based on observed wavenumber and frequency spectra for fetch-limited condition a model is proposed for the form of the directional wavenumber spectrum slice in the dominant wave direction. Reduced wavenumber and frequency spectra are calculated from this model, assuming an empirical spectral directional spreading function and the linear gravity wave dispersion relation. These calculations reveal the underlying influences which shape these reduced spectra. In the energy containing subrange, just above the spectral peak, the dominant influence shaping these spectra is the variation of the directional spreading function with distance from the spectral peak. For frequency spectra, at higher frequencies, the model calculations predict that the range of observed frequency spectral dependences is due primarily to the Doppler shifting from advection of the shorter waves by the orbital motion of the dominant waves, with possible additional influences of wind drift and ambient currents.

Combining these results, composite calculated frequency spectra and one-dimensional wavenumber spectra show close correspondence with measured field spectra. In addition to clarifying the key processes that shape different regimes in the frequency spectrum, a refinement of the bounds of the gravity equilibrium subrange is proposed.

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