title: Soliton turbulence in shallow water ocean surface waves.
abstract: 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.
authors.affiliation: Aix-Marseille Université, CNRS/INSU, IRD, MIO, UM 110, 13288 Marseille Cedex 9, France and Université de Toulon, CNRS/INSU, IRD, MIO, UM 110, 83957 La Garde, France.
authors.forename: Andrea
authors.initials: A
authors.lastname: Costa
authors.affiliation: Nonlinear Waves Research Corporation, Arlington, Virginia 22203, USA.
authors.forename: Alfred R
authors.initials: AR
authors.lastname: Osborne
authors.affiliation: Department of Ocean Engineering, University of North Florida, Jacksonville, Florida 32224-7699, USA.
authors.forename: Donald T
authors.initials: DT
authors.lastname: Resio
authors.affiliation: Dipartimento di Fisica, Universitá di Torino, Torino 10125, Italy.
authors.forename: Silvia
authors.initials: S
authors.lastname: Alessio
authors.affiliation: Dipartimento di Fisica, Universitá di Torino, Torino 10125, Italy.
authors.forename: Elisabetta
authors.initials: E
authors.lastname: Chrivì
authors.affiliation: Université Nice Sophia Antipolis, LPMC, UMR 7336, 06100 Nice, France.
authors.forename: Enrica
authors.initials: E
authors.lastname: Saggese
authors.affiliation: Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA.
authors.forename: Katinka
authors.initials: K
authors.lastname: Bellomo
authors.affiliation: U.S. Army Engineer Research and Development Center, Vicksburg, Mississippi, USA.
authors.forename: Chuck E
authors.initials: CE
authors.lastname: Long