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The Dispersion Relation of Short Wind Waves from Space–Time Wave Measurements

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  • 1 Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi
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Abstract

To study the dispersion relation of short wind waves, a linear wave gauge array (WGA) is configured and mounted on a wave-following buoy to conduct in situ space–time measurements of short gravity waves. Results from two field deployments of the WGA buoy in growing seas are presented. The two-dimensional (2D) wavenumber–frequency spectra derived from the space–time measurements provide a direct examination on the relation of wave frequency and wavenumber of short waves in the along-wind direction. Both wavenumber-based and frequency-based phase velocities are extracted from the 2D spectra. The effect of higher harmonics resulting from the Fourier decomposition of nonlinear wave profiles is more prominent to the frequency-based phase velocity than the wavenumber-based phase velocity. The wavenumber-based phase velocity is consistent with that according to the linear dispersion relation, while the frequency-based phase velocity becomes larger due to the higher harmonics.

Corresponding author address: Dr. David W. Wang, Meso- and Finescale Ocean Physics Section, Department of the Navy, Naval Research Laboratory, Code 7330, Stennis Space Center, MS 29529-5004. Email: dwang@nrlssc.navy.mil

Abstract

To study the dispersion relation of short wind waves, a linear wave gauge array (WGA) is configured and mounted on a wave-following buoy to conduct in situ space–time measurements of short gravity waves. Results from two field deployments of the WGA buoy in growing seas are presented. The two-dimensional (2D) wavenumber–frequency spectra derived from the space–time measurements provide a direct examination on the relation of wave frequency and wavenumber of short waves in the along-wind direction. Both wavenumber-based and frequency-based phase velocities are extracted from the 2D spectra. The effect of higher harmonics resulting from the Fourier decomposition of nonlinear wave profiles is more prominent to the frequency-based phase velocity than the wavenumber-based phase velocity. The wavenumber-based phase velocity is consistent with that according to the linear dispersion relation, while the frequency-based phase velocity becomes larger due to the higher harmonics.

Corresponding author address: Dr. David W. Wang, Meso- and Finescale Ocean Physics Section, Department of the Navy, Naval Research Laboratory, Code 7330, Stennis Space Center, MS 29529-5004. Email: dwang@nrlssc.navy.mil

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