Richardson's Laws for Relative Dispersion in Colored-Noise Flows with Kolmogorov-type Spectra

TL;DR

This paper rigorously proves generalized Richardson's laws for pair dispersion in velocity fields with power-law spectra and wave-number dependent correlation times, extending classical turbulence dispersion laws.

Contribution

It establishes a family of limit theorems for small-scale pair dispersion in colored-noise flows with Kolmogorov-type spectra, including the classical Richardson's laws as a special case.

Findings

Proved limit theorems for pair dispersion in colored-noise flows.

Established a family of generalized Richardson's laws.

Connected classical Richardson's $t^3$ and 4/3-laws to the generalized framework.

Abstract

We prove limit theorems for small-scale pair dispersion in velocity fields with power-law spatial spectra and wave-number dependent correlation times. This result establishes rigorously a family of generalized Richardson's laws with a limiting case corresponding to Richardson's $t^3$ and 4/3-laws.