Field observation of soliton gases in the deep open ocean

Abstract

Soliton gases are large ensembles of random solitons with distinct characteristics arising from integrable system dynamics. They have been widely studied in theory and experiments, and were observed in natural lagoons. However, it remains an open question whether they occur naturally in the open ocean. Nonlinear ocean states containing solitons have been observed in the literature, but the dominance of solitons over other wave components required for a soliton gas has not been demonstrated. Our study provides the first field evidence of soliton gas sea states in the deep ocean, measured in Taiwan waters. The soliton energy ratio derived from the nonlinear Fourier transform (NFT) is employed as a key parameter to quantify how close sea states are to soliton gases. We identify eleven measurements with extremely high soliton energy ratios. They are characterized by short-period waves with relatively small wave heights, accompanied by extreme steepness and Benjamin-Feir Index (BFI) values. These states are exceptionally rare, representing only 0.054 percent of our dataset. Since directional interference can artificially increase the soliton energy ratio, we furthermore apply a probabilistic directional filtering method to remove the directional interference. Three wave records from the Eluanbi station are found to retain high soliton energy ratios after the directional interference has been removed, confirming that they are indeed soliton gases.

Figures (4)

• Figure 1: Data collection from buoy measurements in Taiwanese waters. (A) Locations of three buoy stations, Eluanbi (south), Gueishandao (northeast) and Xiaoliuqiu (southwest). (B) Example of a soliton gas (surface elevation time series) recorded at the Eluanbi station on 2019/05/16 at 14:00. (C) Corresponding directional wave spectrum.
• Figure 2: NFT analysis of a sea state with high soliton energy ratio. (A) Soliton spectrum. (B) Corresponding initial surface wave elevation (black) compared with soliton time series (red) reconstructed from the soliton spectrum.
• Figure 3: Statistical properties of seas states with high soliton energy ratios of at least $0.9$ (red) compared with all data (black) at Eluanbi (A–D), Gueishandao (E–H), and Xiaoliuqiu (I–L). (A), (E), (I): scatter plots of significant wave height $H_s$ versus peak period $T_p$; (B), (F), (J): abnormality index ($AI$) versus directional spreading $\sigma_\theta$; (C), (G), (K): kurtosis versus skewness; (D), (H), (L): wave steepness versus Benjamin–Feir Index (BFI).
• Figure 4: Investigation of reduced directional effects on field-measured soliton gases: distribution of soliton energy ratios for the 11 soliton gas cases after directional filtering with 100 sets of random phases per case. Violin plots show the analyzed soliton energy ratio for: the initial wave field (blue), retention angle $\Delta\theta = 36^\circ$ (orange), and retention angle $\Delta\theta = 20^\circ$ (yellow).