Cascade inverse et dispersion turbulente en turbulence bidimensionnelle

The single-particle dispersion, Lagrangian structure functions and Lagrangian energy spectra characteristic of two-dimensional incompressible turbulent flows are investigated theoretically and numerically. The domain of validity of the classical asymptotic estimates is extended; it is shown in particular that the asymptotic behavior of the single-particle dispersion at small times remains valid throughout the whole self-similar range when the Lagrangian energy spectrum is steeper than w'. Straightforward estimates of the Lagrangian integral time scale TL and the diffusion coefficient at large times "K, based on energy and enstrophy, are proposed; to some extent, they remain valid locally, which allows an analysis of the spatial variability of TL and 9i, within a single turbulent field. Finally, the detrimental effect of artificial numerical diffusion on the numerical simulation of Lagrangian statistics is highlighted and discussed.