We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodicquasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ∼ω −1 . We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ∼ω −1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian. The physical basis of weak wave turbulence was developed by Zakharov and Filonenko [1]. They investigated the theoretical power spectrum for ocean surface waves and demonstrated that in deep water the direct cascade of energy-from the spectral peak to higher frequencies in the spectral tail-should be of the form EðωÞ ∼ ω −4 . This theoretical result was confirmed in subsequent work [2,3] in which the power law was found to be an exact solution of the kinetic equation for the waves. The expansion used in this computation is only up to the third order in wave steepness and thus the theory is referred to as "weak turbulence." Both numerical and experimental confirmations have been found [4][5][6][7][8][9][10]. Zakharov [2,3] also found the Kolmogorov spectrum for shallow water weak wave turbulence. The inverse cascade of wave action to large scale or small frequency is a power law: I ω ∼ Q 1=3 ω −1 , where Q is the flux of action.The theory of integrable soliton turbulence, as used here to analyze ocean wave data, is based on the discovery of complete integrability for the Korteweg-deVries (KdV) equation:, for h the water depth, g the gravitational acceleration), valid for small but finite amplitude, long waves in shallow water. KdV is integrated by the inverse scattering transform (IST) on the infinite line [11]. Zakharov has studied this shallow water case [12,13] for integrable turbulence for a rarified soliton gas. He derived a soliton-gas kinetic equation for the KdV equation using the IST. More recently, the kinetic equation for a dense soliton gas for integrable nonlinear wave equations has been found by El and Kamchatnov [14] by taking the thermodynamic limit of the Wh...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.