Eddy diffusivity of short-correlated random flows: helicity, molecular-diffusion & mean-streaming effects

We study analytically the eddy-diffusivity tensor of a fluid particle in a random flow endowed with a short correlation time. By means of multiple-scale expansion and functional analysis, we obtain the principal contributions to the effective diffusivity induced by each single physical effect and by their interplay. Namely, beside molecular diffusion and a constant uniform mean streaming, we take into account the possibility for the (Gaussian, stationary, homogeneous, isotropic, incompressible) turbulent fluctuations to break parity invariance. With respect to the well-known boost of diffusivity driven by turbulence for delta-correlated flows, we find that the presence of a short temporal correlation of positive type brings about a diffusivity depletion, both when alone and even when coupled with the aforementioned effects, with two main 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. Even more importantly, opposite findings can arise when negative temporal correlations are allowed.