Titre/Title : ON THE STOCHASTIC MODELING OF THE SPATIO-TEMPORAL STRUCTURE OF HOMOGENEOUS AND ISOTROPIC TURBULENCE
Contact : Nicolas Mordant (équipe EDT)
Résumé/Abstract : We propose to analyse and model, using random fields, the spatio-temporal structure of homogeneous and isotropic turbulence. We begin with a standard analysis of the statistical properties of the velocity field by estimating the spatio-temporal correlations of the Eulerian velocity, as well as the generalized spatio-temporal structure functions at orders 2, 3 and 4. To do so, we use the simulation that is stored (and made available to the community) at Johns Hopkins University. In a second stage of this work, we propose a stochastic modeling of such a spatio-temporal field, in the spirit of what has been done for the (purely) spatial velocity. This includes a precise characterization of the correlation structure of the field as it can be reproduced by a Gaussian approximation, that we modify using a multifractal measure in order to reproduce non-Gaussian features, as they are demanded by the observed high level of skewness and flatness of increments. This study, once generalized to three spatial dimensions, incorporating furthermore the incompressibility constraint, gives an example of a synthetic advecting velocity field, in which particle dispersion could be investigated.