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

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.