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

• Published in: Journal of statistical mechanics Vol. 2016; no. 10; pp. 103205 - 103221
• Main Authors: Martins Afonso, Marco, Mazzino, Andrea, Gama, Sílvio
• Format: Journal Article
• Language: English
• Published: IOP Publishing and SISSA 19.10.2016
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/2016/10/103205

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.