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P. Héas, D. Heitz, E. Mémin. Evidence of turbulence power laws from image data. In International Conference and Advanced School "Turbulent Mixing and Beyond", The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, 2009.


Based on energy cascades describing the multi-scale structure of turbulent motion, we propose an inverse motion modeling method able to infer the most evident power laws model given some image sequence. Inference relies on the spatial regularization principle, used in image velocimetry techniques in order to cure the ill-posed inverse motion estimation problem. Regularization is adapted here to the case of power laws behaviors occurring in bi-dimensional or quasi bi-dimensional flows: motion increments are constrained to behave through scales as the most likely self-similar process given the data. More precisely, in a first level of inference, motion estimation formulated as a hard constrained minimization problem is optimally solved by taking advantage of lagrangian duality. It results in a collection of first-order spatial regularizers acting at different scales. This estimation is non-parametric since the optimal regularization parameters at the different scales are obtained by solving the dual problem. In a second level of inference, the most likely self-similar model given the data is optimally selected by maximization of bayesian evidence. The motion estimator accuracy is first evaluated on a synthetic image sequence of simulated bi-dimensional turbulence and then on a real meteorological image sequence. Results obtained with the proposed physical based approach exceeds the best state of the art results. Furthermore, selecting from images the most evident power law model enables the recovery of energy dissipation rate and other physical quantities which are of major interest for turbulence characterization


Dominique Heitz
Etienne Mémin

BibTex Reference

   Author = {Héas, P. and Heitz, D. and Mémin, E.},
   Title = {Evidence of turbulence power laws from image data},
   BookTitle = {International Conference and Advanced School "Turbulent Mixing and Beyond"},
   Address = {The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy},
   Year = {2009}

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