New scaling laws predicting turbulent particle pair diffusion, overcoming the limitations of the prevalent Richardson–Obukhov theory

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.