[A-CG47] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

[ACG47-P10] Verification of the nonlinear dispersion relation of free waves in the open ocean

*Yukiharu Hisaki¹ (1.University of the Ryukyus)

Keywords:wave, dispersion relation, nonlinear

According to the nonlinear theory of surface waves, surface waves are composed of free waves and bound waves corresponding to the second harmonic. Among these, free waves satisfy a linear dispersion relation. However, as is known from Stokes wave theory, the dispersion relation includes contributions of amplitudes. In the open ocean, where ocean surface waves can be regarded as deep water waves, the width of the ocean wave spectrum is wide and nonlinearity is small, so it is not even easy to detect bound waves from sea surface measurements. High-frequency (HF) ocean radar measures the Doppler spectrum. This Doppler spectrum is almost proportional to the three-dimensional wave spectrum (a spectrum expressed as a function of frequency and horizontal wave number vector) values at the Bragg wave number vector (horizontal wave number vector, which is -2 times the horizontal incident radio wave number vector). This makes it easy to distinguish between free and bound waves in ocean surface waves. It is also possible to verify the dispersion relation of free waves from the spectral peak frequency of free waves. In previous studies, only cases of waves traveling in a single direction were used to verify nonlinear dispersion relations. This is not appropriate for the case of the open ocean, which is composed of wave components that propagate in multiple directions. Therefore, we verified the nonlinear dispersion relation for random waves that propagate in multiple directions. First, we calculated the frequency from the nonlinear dispersion relation by setting the horizontal wave number vector to a fixed value. The deviation from the linear dispersion relation was expressed as a function of the mean wave direction and wave height in the ocean wave spectrum. It was found that the frequency deviation reached a maximum at a certain wave height. Next, the dispersion relation of free waves was verified using the HF radar Doppler spectrum. The wave spectrum used was the ERA5 spectrum. In addition, to eliminate the effects of ocean currents, we used current velocity data at a depth of 4 m below the water surface. The correlation between the velocity obtained from the difference between the Doppler spectrum peak frequency and the linear dispersion relation and the radial current velocity was about 0.9. Furthermore, we investigated the difference between these differences and the deviation from the linear dispersion relationship of the nonlinear dispersion relationship. Although this correlation was not high, when we compared only cases where the ERA5 spectrum values were considered appropriate, this correlation was higher.