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Multiscale geometric analysis of turbulence by curvelets

Jianwei Ma 1 M. Yussuf Hussaini 2 Oleg Vasilyef 3 François-Xavier Le Dimet 4
4 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : In this paper, after a brief review of curvelets and their relation to classical wavelet transform, multiscale geometric analysis is systematically applied to turbulent flows in two and three dimensions. The analysis is based on the constrained minimization of a total variation functional representing the difference between the data and its representation in the curvelet space. Constrained multiscale minimization results in a minimum loss of the geometric flow features and the extraction of the coherent structures with their edges and geometry properly preserved, which is significant for turbulence modeling. The effectiveness of curvelet analysis compared to the wavelet transform is demonstrated for both two- and three-dimensional turbulent flows.
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Jianwei Ma, M. Yussuf Hussaini, Oleg Vasilyef, François-Xavier Le Dimet. Multiscale geometric analysis of turbulence by curvelets. Physics of Fluids, American Institute of Physics, 2009, 21 (7), pp.075104:1-19. ⟨10.1063/1.3177355⟩. ⟨inria-00391872⟩



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