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We analytically investigate the effective-diffusivity tensor of a tracerparticle in a fluid flow endowed with a short correlation time. By means offunctional calculus and a multiscale expansion, we write down the maincontributions to the eddy diffusivity due to each single physical effect and totheir interplays. Namely, besides molecular diffusivity and a constant uniformmean streaming, we take into account the possibility for the (incompressible,Gaussian, stationary, homogeneous, isotropic) turbulent fluctuations to breakparity invariance. With respect to the classical turbulence-driven diffusivityamplification for delta-correlated flows, we find that the presence of a shorttemporal 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 theinterference between molecular diffusion and mean flow.

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