[Filtrage en ondelettes orthogonales pour lʼétude de la turbulence dans les plasmas : Comparaison entre la méthode CVE et la méthode POD]
Cet article compare deux méthodes permettant dʼextraire les contributions cohérentes dans les écoulements turbulents : la méthode CVE (Coherent Vorticity Extraction), basée sur la représentation en ondelettes, et la méthode POD (Proper Orthogonal Decomposition). La première méthode, CVE, décompose lʼécoulement en base dʼondelettes orthogonales puis, grâce au filtrage des coefficients dʼondelettes, permet de séparer lʼécoulement entre une contribution cohérente ayant un comportement statistique non Gaussien et un écoulement résiduel aléatoire ne présentant pas de structures. La seconde méthode, POD, est basée sur la décomposition en valeurs singulières. Elle décompose lʼécoulement dans la base de fonctions qui retient le mieux lʼénergie dʼun ensemble de réalisations de lʼécoulement. Ces deux méthodes sont ensuite utilisées pour analyser les résultats de simulations numériques directes calculant un écoulement turbulent bidimensionnel dʼondes de dérive, gouverné par lʼéquation dʼHasegawa–Wakatani, ceci pour deux cas limites : le régime quasi-hydrodynamique et le régime quasi-adiabatique. Les résultats sont comparés en fonction des taux de compression, des proportions dʼenstrophie et de flux radial retenues, ainsi que du spectre dʼenstrophie (statistique dʼordre deux) et de statistiques dʼordre plus élévé.
We assess two techniques for extracting coherent vortices out of turbulent flows: the wavelet based Coherent Vorticity Extraction (CVE) and the Proper Orthogonal Decomposition (POD). The former decomposes the flow field into an orthogonal wavelet representation and subsequent thresholding of the coefficients allows one to split the flow into organized coherent vortices with non-Gaussian statistics and an incoherent random part which is structureless. POD is based on the singular value decomposition and decomposes the flow into basis functions which are optimal with respect to the retained energy for the ensemble average. Both techniques are applied to direct numerical simulation data of two-dimensional drift-wave turbulence governed by Hasegawa–Wakatani equation, considering two limit cases: the quasi-hydrodynamic and the quasi-adiabatic regimes. The results are compared in terms of compression rate, retained energy, retained enstrophy and retained radial flux, together with the enstrophy spectrum and higher order statistics.
Mots-clés : POD, Ondelettes, Turbulence plasma, Structures cohérentes
Shimpei Futatani 1 ; Wouter J.T. Bos 2 ; Diego del-Castillo-Negrete 3 ; Kai Schneider 4 ; Sadruddin Benkadda 1 ; Marie Farge 5
@article{CRPHYS_2011__12_2_123_0,
author = {Shimpei Futatani and Wouter J.T. Bos and Diego del-Castillo-Negrete and Kai Schneider and Sadruddin Benkadda and Marie Farge},
title = {Coherent vorticity extraction in resistive drift-wave turbulence: {Comparison} of orthogonal wavelets versus proper orthogonal decomposition},
journal = {Comptes Rendus. Physique},
pages = {123--131},
publisher = {Elsevier},
volume = {12},
number = {2},
year = {2011},
doi = {10.1016/j.crhy.2010.12.004},
language = {en},
}
TY - JOUR AU - Shimpei Futatani AU - Wouter J.T. Bos AU - Diego del-Castillo-Negrete AU - Kai Schneider AU - Sadruddin Benkadda AU - Marie Farge TI - Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition JO - Comptes Rendus. Physique PY - 2011 SP - 123 EP - 131 VL - 12 IS - 2 PB - Elsevier DO - 10.1016/j.crhy.2010.12.004 LA - en ID - CRPHYS_2011__12_2_123_0 ER -
%0 Journal Article %A Shimpei Futatani %A Wouter J.T. Bos %A Diego del-Castillo-Negrete %A Kai Schneider %A Sadruddin Benkadda %A Marie Farge %T Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition %J Comptes Rendus. Physique %D 2011 %P 123-131 %V 12 %N 2 %I Elsevier %R 10.1016/j.crhy.2010.12.004 %G en %F CRPHYS_2011__12_2_123_0
Shimpei Futatani; Wouter J.T. Bos; Diego del-Castillo-Negrete; Kai Schneider; Sadruddin Benkadda; Marie Farge. Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition. Comptes Rendus. Physique, Propagation and plasmas: new challenges, new applications, Volume 12 (2011) no. 2, pp. 123-131. doi : 10.1016/j.crhy.2010.12.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.12.004/
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