Lagrangian time-scales in homogeneous non-Gaussian turbulence

Lagrangian time-scales in homogeneous non-Gaussian turbulence were studied using a one-dimensional Lagrangian Stochastic Model. The existence of two time-scales tau(L) and T-L, one typical of the inertial subrange and the other which is an integral property, is outlined. Variations of the ratio T-L/tau(L) in the plane skewness-flatness (S, F) are shown and a connection with the statistical constraint F greater than or equal to S-2 + 1 is evidenced. The Lagrangian autocorrelation function rho(t) of particle velocity was computed for some values of (S, F). It is shown that for small times, say t < T-L, the influence of non-Gaussianity is negligible and rho(t) presents the same behaviour as in the Gaussian case regardless of variations in (S, F). As the time increases, departures from Gaussianity are observed and autocorrelation turns out to be always larger than in the Gaussian case. This is supported by some considerations in terms of information entropy, which is shown to decrease with increasing departures from Gaussianity. Spectral analysis of Lagrangian velocity shows that non-Gaussianity is relevant only to large scales of the stochastic process and that the expected inertial subrange decay omega(-2) is attained by spectra of all simulations, except for one case in which the model probability density function is bimodal, due to the vicinity to the statistical limit.