Comptes Rendus
Analysis of random nonlinear water waves: the Stokes–Woodward technique
Comptes Rendus. Mécanique, Volume 331 (2003) no. 3, pp. 189-196.

A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Considering laboratory wind generated water waves, comparisons between the presented generalization and more standard techniques allow to extract the spectral energy due to nonlinear wave–wave interactions. It is shown that our analysis extends the domain of standard spectral estimation techniques from narrow-band to broad-band processes.

Une généralisation du théorème de Woodward est appliquée au cas d'un signal aléatoire modulé en amplitude et en fréquence. Le spectre du signal ainsi qu'une estimation robuste du bispectre sont obtenues grace à cette nouvelle technique. En sus, des moments statistiques d'ordre supérieur quantifiant l'énergie due aux non linéarités, i.e., aux interactions entre vagues dans le cas des ondes de surface, sont évalués. L'énergie spectrale d'interaction non linéaire est extraite grâce à la comparaison de la présente méthode, à des méthodes plus classiques lors de l'analyse de signaux de vagues de vent fort générées en soufflerie. Il est finalement montré que notre technique étend le domaine des méthodes d'estimation spectrale aux processus large bande.

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DOI: 10.1016/S1631-0721(03)00055-X
Keywords: Fluid mechanics, Mode coupling, Wave–wave interaction, Horizontal asymmetry, Vertical asymmetry, Bispectrum, Amplitude modulation, Frequency modulation
Mot clés : Mécaniques des fluides, Couplage de mode, Interaction vague–vague, Dissymétrie verticale, Dissymétrie horisontale, Bispectre, Modulation d'amplitude, Modulation de fréquence

Tanos Elfouhaily 1; Maminirina Joelson 1; Stéphan Guignard 1; Hubert Branger 1; Donald R. Thompson 2; Bertrand Chapron 3; Douglas Vandemark 4

1 Centre national de la recherche scientifique (CNRS), institut de recherche sur les phénomènes hors equilibre (IRPHE), Marseille, France
2 The Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA
3 Département d'océanographie spatiale, IFREMER, centre de Brest, BP 70, 29280 Plouzané, France
4 NASA Goddard Space Flight Center, Laboratory for Hydrospheric Processes, Wallops Island, VA 23337, USA
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     title = {Analysis of random nonlinear water waves: the {Stokes{\textendash}Woodward} technique},
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Tanos Elfouhaily; Maminirina Joelson; Stéphan Guignard; Hubert Branger; Donald R. Thompson; Bertrand Chapron; Douglas Vandemark. Analysis of random nonlinear water waves: the Stokes–Woodward technique. Comptes Rendus. Mécanique, Volume 331 (2003) no. 3, pp. 189-196. doi : 10.1016/S1631-0721(03)00055-X. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00055-X/

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