Combined role of molecular diffusion, mean streaming and helicity in the eddy diffusivity of short-correlated random flows

TL;DR

This paper analytically examines how molecular diffusion, mean streaming, and helicity influence the eddy diffusivity of a tracer in short-correlated random flows, revealing that short correlation times generally reduce diffusivity except when helicity or mean flow interactions are involved.

Contribution

It provides a detailed analytical framework quantifying the individual and combined effects of physical mechanisms on eddy diffusivity in short-correlated turbulent flows.

Findings

Short correlation times tend to decrease eddy diffusivity.

Helicity and mean flow interactions can enlarge diffusivity perturbatively.

Interference between molecular diffusion and mean flow enhances diffusivity.

Abstract

We analytically investigate the effective-diffusivity tensor of a tracer particle in a fluid flow endowed with a short correlation time. By means of functional calculus and a multiscale expansion, we write down the main contributions to the eddy diffusivity due to each single physical effect and to their interplays. Namely, besides molecular diffusivity and a constant uniform mean streaming, we take into account the possibility for the (incompressible, Gaussian, stationary, homogeneous, isotropic) turbulent fluctuations to break parity invariance. With respect to the classical turbulence-driven diffusivity amplification for delta-correlated flows, we find that the presence of a short temporal correlation induces a diminution even when coupled with such effects, with two principal exceptions. Notably, the diffusivity is --- perturbatively --- enlarged not only by the helical contribution itself, but also by the interference between molecular diffusion and mean flow.