Three-wave and four-wave interactions in gravity wave turbulence

Type Publication
Date 2017-11
Language English
Copyright 2017 American Physical Society
Author(s) Aubourg Quentin1, Campagne Antoine1, Peureux Charles2, Ardhuin FabriceORCID3, Sommeria Joel1, Viboud Samuel1, Mordant Nicolas1
Affiliation(s) 1 : Univ Grenoble Alpes, CNRS, Lab Ecoulements Geophys & Ind, F-38000 Grenoble, France.
2 : Univ Brest, CNRS, IFREMER, Lab Oceanog Phys & Spatiale,IRD, F-29200 Plouzane, France.
Source Physical Review Fluids (2469-990X) (Amer Physical Soc), 2017-11 , Vol. 2 , N. 11 , P. 114802 (1-19)
DOI 10.1103/PhysRevFluids.2.114802
Abstract

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015)]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

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