Geodesic
Divergence-free Wavelets for Coherent Vortex Extraction in 3D homogeneous isotropic turbulence
Erwan Deriaz1 ; Margarete O. Domingues2, 3, 4 ; Valérie Perrier1 ; Kai Schneider3 ; Marie Farge4
1 Laboratoire de Modélisation et Calcul de l'IMAG, BP 53, 38041 Grenoble cedex 9, France.
2 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.
3 MSNM–CNRS & CMI, Université de Provence, 39 rue Joliot–Curie, 13453 Marseille cedex 13, France.
4 LMD–CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris cedex 05, France.
ESAIM. Proceedings, Tome 16 (2007), pp. 146-163.

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In this paper we investigate the use of divergence-free wavelet bases for the Coherent Vortex Extraction (CVE) of turbulent flows. We begin with a short presentation of the construction of 3D divergence-free biorthogonal wavelets. We apply the CVE decomposition to a homogeneous isotropic turbulent flow, computed by a Direct Numerical Simulation (DNS) at resolution 2403 and upsampled to . First, the CVE is applied to the vorticity field. Using the divergence-free wavelets for the vorticity field makes sense since the vorticity also verifies an incompressibility condition when the velocity does.
The coherent part of the vorticity field is reconstructed from the largest wavelet coefficients, corresponding to , while the complement constitutes the incoherent part. We show that the coherent part corresponds to the vortex tubes of the flow and retains most of the energy and enstrophy. These results are then compared to those obtained using non–divergent free wavelets, both orthogonal and biorthogonal ones. Then we also apply the CVE method, using divergence-free wavelets, to decompose the velocity field and subsequently compute the corresponding vorticity fields. The results show that the decomposition of velocity exhibit large smooth vortex structures in contrast to what is obtained with the decomposition of the vorticity.

DOI : 10.1051/proc:2007011

Erwan Deriaz 1 ; Margarete O. Domingues 2, 3, 4 ; Valérie Perrier 1 ; Kai Schneider 3 ; Marie Farge 4

1 Laboratoire de Modélisation et Calcul de l'IMAG, BP 53, 38041 Grenoble cedex 9, France.
2 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.
3 MSNM–CNRS & CMI, Université de Provence, 39 rue Joliot–Curie, 13453 Marseille cedex 13, France.
4 LMD–CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris cedex 05, France. 
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     title = {Divergence-free {Wavelets} for {Coherent} {Vortex} {Extraction} in {3D} homogeneous isotropic turbulence},
     journal = {ESAIM. Proceedings},
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Erwan Deriaz; Margarete O. Domingues; Valérie Perrier; Kai Schneider; Marie Farge. Divergence-free Wavelets for Coherent Vortex Extraction in 3D homogeneous isotropic turbulence. ESAIM. Proceedings, Tome 16 (2007), pp. 146-163. doi : 10.1051/proc:2007011. http://geodesic.mathdoc.fr/articles/10.1051/proc:2007011/

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