Soliton Turbulence in Shallow Water Ocean Surface Waves
Résumé
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 periodic-quasiperiodic 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.
Mots clés
92.10.Hm
92.10.Lq
92.10.Sx
Ocean waves and oscillations
Turbulence diffusion and mixing processes in oceanography
Coastal estuarine and near shore processes
Nonlinear Sciences - Pattern Formation and Solitons
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Physics - Atmospheric and Oceanic Physics
Physics - Data Analysis
Statistics and Probability
Physics - Fluid Dynamics
Domaines
Planète et Univers [physics]
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