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Statistics of surface gravity wave turbulence in the space and time domains

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Nazarenko, Sergey, Lukaschuk, Sergei, McLelland, Stuart and Denissenko, Petr. (2010) Statistics of surface gravity wave turbulence in the space and time domains. Journal of Fluid Mechanics, Vol.642 . pp. 395-420. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112009991820

Abstract

We present experimental results on simultaneous space–time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that the both wavenumber and frequency spectra are not universal and dependent on the wave strength, with some evidence in favour of the WTT at larger wave intensities when the finite-flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (p.d.f.) and the structure functions (SFs). Analysing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-Gaussian p.d.f. core and the low-order SFs and the latter in the p.d.f. tails and the high-order SFs. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than the t-space SFs do. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Engineering Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Gravity waves, Turbulence -- Research, Frequency spectra -- Research, Amplitude modulation
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Official Date:	January 2010
Volume:	Vol.642
Number of Pages:	26
Page Range:	pp. 395-420
Identification Number:	10.1017/S0022112009991820
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Hull Environmental Research Institute (HERI)
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URI:	http://wrap.warwick.ac.uk/id/eprint/2571