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Soliton Turbulence in Shallow Water Ocean Surface Waves

Andrea Costa, Alfred R. Osborne, Donald T. Resio, Silvia Alessio, Elisabetta Chrivì, Enrica Saggese, Katinka Bellomo, and Chuck E. Long
Phys. Rev. Lett. 113, 108501 – Published 2 September 2014
Physics logo See Focus story: New Type of Turbulence on North Carolina’s Coast

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 ω1. 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 ω1 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.

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  • Received 3 March 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.108501

© 2014 American Physical Society

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New Type of Turbulence on North Carolina’s Coast

Published 2 September 2014

Analysis of sea surface height measurements during a storm in North Carolina’s Outer Banks has led to the first observation of an unusual form of turbulence.

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Authors & Affiliations

Andrea Costa1,*, Alfred R. Osborne2,†, Donald T. Resio3, Silvia Alessio4, Elisabetta Chrivì4, Enrica Saggese5, Katinka Bellomo6, and Chuck E. Long7,‡

  • 1Aix-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
  • 2Nonlinear Waves Research Corporation, Arlington, Virginia 22203, USA
  • 3Department of Ocean Engineering, University of North Florida, Jacksonville, Florida 32224-7699, USA
  • 4Dipartimento di Fisica, Universitá di Torino, Torino 10125, Italy
  • 5Université Nice Sophia Antipolis, LPMC, UMR 7336, 06100 Nice, France
  • 6Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA
  • 7U.S. Army Engineer Research and Development Center, Vicksburg, Mississippi, USA

  • *andrea.costa@univ-amu.fr
  • Corresponding author. al.osborne@gmail.com
  • Retired.

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Issue

Vol. 113, Iss. 10 — 5 September 2014

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