Physics of Fluids, Volume 33, Issue 3, March 2021. Both the evolution of particle pair separation distance l in a turbulent flow and how different length scales affect l are major unresolved challenges. The reigning theory in this topic is that of Richardson and Obukhov (R-O theory). We propose a new theory of pair diffusion in homogeneous, isotropic turbulence hypothesizing that not only structures of size l, but much larger ones also induce significant pair separation—ignored in the R-O theory. We arrive at new scaling laws for the pair diffusivity K, leading to [math] where γ depends on the size of the inertial subrange: for a short inertial subrange, we find from our simulations that [math], and for an infinite inertial subrange, we find that [math]—these relations agree closely with data. We assert that the celebrated “R-O constant” gl is neither physically meaningful nor a constant as universally assumed; our theory leads to two new physically relevant constants: GK for pair diffusivity and Gl for pair separation—which asymptote to [math] and [math] at high Reynolds numbers. We find that the particle dispersion is smaller by an order of magnitude compared to R-O prediction; this is significant in many applications such as sprays, and, in particular, the spread of biological contagions (e.g., COVID19) which persist longer and drift farther compared to R-O prediction. We find that the turbulent dispersion does not depend on the fine structure timescale—a striking result which would greatly facilitate turbulent diffusion modeling.

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