Is Isotropic Turbulent Diffusion Symmetry Restoring?

Analytic expressions of the convection diffusivity tensor in fully developed isotropic turbulent flow are given and used to evaluate the broadening of a cloud of marked particle pairs perpendicular and longitudinal with respect to an initial separation. Both turn out to remain different because of the difference between $〈v_{\perp }^2〉$ and $〈v_{\parallel }^2〉$. Parameter-free expressions for the variances ${\sigma }_{\perp }$ and ${\sigma }_{\parallel }$ yield the dependence on the Reynolds number and other flow parameters in addition to the known scaling behavior $\propto {\tau }^{3-\gamma }$.