Measurement of the High-Frequency Spectrum of Ocean Surface Waves

Abstract

High-frequency spectra of wind-generated ocean waves were measured at an ocean research tower of Kyushu University using a fast-response wave recorder and an electronic differentiating circuit. Wind waves generated by a northeast wind (speed U_10.5=8 m s⁻¹, fetch F=2 km) were superimposed on the swell from the north and in a stationary state. The equilibrium range of the wave spectrum, where the spectral form is given bywas clearly observed in a frequency range f_m<f≤4 Hz of the measured spectrum, where g is the acceleration of gravity and f_m the spectral peak frequency. The measured value of the equilibrium constant β was 0.016 for the dimensionless fetch F̂ (=gF/U_*²=1.3×10⁵ (where U_* is the friction velocity of the wind), which was very close to the value obtained by Burling (1959). However, the equilibrium spectrum of the gravity wave range occurred only below 4 Hz, and the spectral form in the gravity-capillary range (f>5 Hz) was given approximately by>where σ is the surface tension, ρw the density of water and k the wavenumber. The measured value of the dimensionless constant α_g was 0.012 for the frequency range 6 Hz≤f≤14 Hz of the measured spectrum, which was very close to the values measured in our laboratory experiment (U_r≈40 cm s⁻¹ at F=5.85 m and 8.26 m). The result confirmed that the spectral form in the gravity-capillary range is really independent of the fetch.