Geodesic
Coherent vortex extraction in 3D homogeneous isotropic turbulence using orthogonal wavelets
Margarete O. Domingues1, 2, 3 ; Ingmar Broemstrup4 ; Kai Schneider2, 5 ; Marie Farge1 ; Benjamin Kadoch2
1LMD-IPSL-CNRS, Ecole Normale Supérieure 24, rue Lhomond, 75231 Paris, Cedex 05, France.
2Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), CNRS and Universités d'Aix-Marseille, 38, rue F. Joliot-Curie, 13451 Marseille Cedex 20, France.
3Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brazil.
4Center for Multiscale Plasma Dynamics (CMPD), University of Maryland, College Park, MD 20742, USA.
5Centre de Mathématiques et d'Informatique (CMI), Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France.
ESAIM. Proceedings, Tome 16 (2007), pp. 164-180
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The coherent vortex extraction (CVE) decomposes each turbulent flow realization into two orthogonal components: a coherent and a random incoherent flow. They both contribute to all scales in the inertial range, but exhibit different statistical behaviour. The CVE decomposition is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. We decompose a 3D homogeneous isotropic turbulent flow at Taylor microscale Reynolds numbers computed by a direct numerical simulation (DNS) at resolution . Only wavelet modes correspond to the coherent flow made of vortex tubes, which contributes to of the enstrophy. Another observation is that the coherent flow exhibits in the inertial range the same slope in the energy spectrum and slope in the enstrophy spectrum as the total flow does. The remaining wavelet modes correspond to a random residual flow which is structureless, quasi equipartition of energy and a Gaussian velocity probability distribution function (PDF). We also analyse and visualize the Lamb vector, its divergence and curl and study the contributions coming from the coherent and incoherent components of vorticity and the induced velocity.
DOI : 10.1051/proc:2007005

Margarete O. Domingues  1 , 2 , 3   ; Ingmar Broemstrup  4   ; Kai Schneider  2 , 5   ; Marie Farge  1   ; Benjamin Kadoch  2

1 LMD-IPSL-CNRS, Ecole Normale Supérieure 24, rue Lhomond, 75231 Paris, Cedex 05, France.
2 Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), CNRS and Universités d'Aix-Marseille, 38, rue F. Joliot-Curie, 13451 Marseille Cedex 20, France.
3 Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brazil.
4 Center for Multiscale Plasma Dynamics (CMPD), University of Maryland, College Park, MD 20742, USA.
5 Centre de Mathématiques et d'Informatique (CMI), Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France. 
@article{EP_2007_16_a11,
     author = {Margarete O. Domingues and Ingmar Broemstrup and Kai Schneider and Marie Farge and Benjamin Kadoch},
     title = {Coherent vortex extraction in {3D} homogeneous isotropic turbulence using orthogonal wavelets},
     journal = {ESAIM. Proceedings},
     pages = {164--180},
     year = {2007},
     volume = {16},
     doi = {10.1051/proc:2007005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2007005/}
}
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%J ESAIM. Proceedings
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Margarete O. Domingues; Ingmar Broemstrup; Kai Schneider; Marie Farge; Benjamin Kadoch. Coherent vortex extraction in 3D homogeneous isotropic turbulence using orthogonal wavelets. ESAIM. Proceedings, Tome 16 (2007), pp. 164-180. doi: 10.1051/proc:2007005

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