Noise small-correlation-time eects on the dispersion of passive scalars

Abstract. { The eect of a small correlation time, , of the (colored-) small-scales noise on the eective diusivities for the transport of passive scalars is investigated. It has recently been shown that the presence of makes the transport problem equivalent to the white-in-time case provided by a renormalized advecting velocity eld. This equivalence is here exploited to investigate, both analytically and perturbatively in the Strouhal number of the advecting velocity eld, the mechanism responsible for enhancement of transport. In the problem of transport of passive elds the main quantity of interest is the rate at which turbulence transports the scalar, e.g. the density of particles or dye injected into the flow. Under general conditions, for times large compared to those characteristic of the turbulent eld, transport is always diusive [1-5] and is characterized by eective diusion coecients, Def, the so-called eddy diusivities. They can be obtained [6], from the Lagrangian viewpoint, in terms of time integral of the Lagrangian velocity correlations via the well-known Taylor’s formula [7]. In ref. [6] and, more recently, in ref. [8] the problem of the interference between turbulent and molecular diusion has been investigated. It concerns the variation of the turbulen