Invariance principle for inertial-scale behavior of scalar fields in Kolmogorov-type turbulence

We prove limit theorems for small-scale pair dispersion in synthetic velocity fields with power-law spatial spectra and wavenumber dependent correlation times. These limit theorems are related to a family of generalized Richardson’s laws with a limiting case corresponding to Richardson’s t3- and 4/3-laws. We also characterize a regime of positive dissipation of passive scalars.