Particle dispersion in a multidimensional random flow with arbitrary temporal correlations
Abstract
We study the statistics of relative distances R(t) between fluid particles in a spatially smooth random flow with arbitrary temporal correlations. Using the space dimensionality d as a large parameter we develop an effective description of Lagrangian dispersion. We describe the exponential growth of relative distances <R ^{2}(t)>∝ exp 2 λ¯t at different values of the ratio between the correlation and turnover times. We find the stretching correlation time which determines the dependence of R_{1}R_{2} on the difference t_{1} t_{2}. The calculation of the next cumulant of R^{2} shows that statistics of R^{2} is nearly Gaussian at small times (as long as d≫1) and becomes lognormal at large times when larged approach fails for highorder moments. The crossover time between the regimes is the stretching correlation time which surprisingly appears to depend on the details of the velocity statistics at t≪ τ. We establish the dispersion of the ln( R^{2}) in the lognormal statistics.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 1998
 DOI:
 10.1016/S03784371(97)004299
 Bibcode:
 1998PhyA..249...36F