[La technique de Stokes–Woodward pour l'analyse de vagues aléatoires non linéaires]
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.
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.
Accepté le :
Publié le :
Mots-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
@article{CRMECA_2003__331_3_189_0,
author = {Tanos Elfouhaily and Maminirina Joelson and St\'ephan Guignard and Hubert Branger and Donald R. Thompson and Bertrand Chapron and Douglas Vandemark},
title = {Analysis of random nonlinear water waves: the {Stokes{\textendash}Woodward} technique},
journal = {Comptes Rendus. M\'ecanique},
pages = {189--196},
publisher = {Elsevier},
volume = {331},
number = {3},
year = {2003},
doi = {10.1016/S1631-0721(03)00055-X},
language = {en},
}
TY - JOUR AU - Tanos Elfouhaily AU - Maminirina Joelson AU - Stéphan Guignard AU - Hubert Branger AU - Donald R. Thompson AU - Bertrand Chapron AU - Douglas Vandemark TI - Analysis of random nonlinear water waves: the Stokes–Woodward technique JO - Comptes Rendus. Mécanique PY - 2003 SP - 189 EP - 196 VL - 331 IS - 3 PB - Elsevier DO - 10.1016/S1631-0721(03)00055-X LA - en ID - CRMECA_2003__331_3_189_0 ER -
%0 Journal Article %A Tanos Elfouhaily %A Maminirina Joelson %A Stéphan Guignard %A Hubert Branger %A Donald R. Thompson %A Bertrand Chapron %A Douglas Vandemark %T Analysis of random nonlinear water waves: the Stokes–Woodward technique %J Comptes Rendus. Mécanique %D 2003 %P 189-196 %V 331 %N 3 %I Elsevier %R 10.1016/S1631-0721(03)00055-X %G en %F CRMECA_2003__331_3_189_0
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/
[1] A nonlinear second-order stochastic model of ocean surface waves, Oceanologica Acta, Volume 24 (2001) no. 5, pp. 1-7
[2] Weakly nonlinear theory and sea state bias estimations, J. Geophys. Res., Volume 104 (1999) no. C4, pp. 7641-7647
[3] Improved electromagnetic bias theory, J. Geophys. Res., Volume 105 (2000) no. C1, pp. 1299-1310
[4] Higher-order hydrodynamic modulation: theory and applications for ocean waves, Proc. Roy. Soc. London Ser. A, Volume 457 (2001) no. 2015, pp. 2585-2608
[5] Improved electromagnetic bias theory: Inclusion of hydrodynamic modulations, J. Geophys. Res., Volume 106 (2001) no. C3, pp. 4655-4664
[6] Harmonic Analysis and the Theory of Probability, University California Press, California, USA, 1960
[7] Wind Waves: Their Generation and Propagation in Ocean Surface, Prentice-Hall, Englewood Cliffs, NJ, USA, 1965
[8] On the joint distribution of wave periods and amplitudes in random wave field, Proc. Roy. Soc. London Ser. A, Volume 389 (1983), pp. 241-258
[9] On narrow-band representation of ocean waves, 1. Theory, J. Geophys. Res., Volume 91 (1986) no. C6, pp. 7743-7752
[10] An Introduction to Statistical Communication Theory, IEEE Press, Piscataway, NJ, 1996
[11] P.M. Woodward, The spectrum of random frequency modulation, Technical memorandum, Telecommunications Research Establishement, Great Malvern, Worcs., England, 1952
[12] Perturbation techniques for random vibration of nonlinear systems, J. Acc. Soc. America, Volume 35 (1963) no. 11, pp. 1700-1705
[13] The spectrum of a high-index fm waveform: Woodward's theorem revisited, IEEE Trans. Comm. Tech., Volume COM-17 (1969) no. 2, pp. 201-207
[14] Digital bispectral analysis and its applications to nonlinear wave interactions, IEEE Trans. Plasma Sci., Volume PS-7 (1979) no. 2, pp. 120-131
[15] Probability distribution applicable to non-Gaussian random processes, Prob. Engrg. Mech., Volume 9 (1994), pp. 255-264
[16] Activities in and preliminary results of air-sea interaction research at I.M.S.T, Adv. Geophys., Volume 16 (1974), pp. 391-405
[17] An efficient algorithm for the zero crossing detection in digitized measurement signal, Measurement, Volume 30 (2001), pp. 187-196
[18] Definitions of instantaneous frequency under physical constraints, J. Franklin Inst., Volume 337 (2000) no. 4, pp. 303-316
[19] Delay-Doppler analysis of bistatically reflected signals from the ocean surface: theory and application, IEEE Trans. Geosci. and Remote Sens., Volume 40 (2002) no. 3, pp. 560-573
Cité par Sources :
Commentaires - Politique