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

Abstract

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 K ∼ l γ where γ depends on the size of the inertial subrange: for a short inertial subrange, we find from our simulations that K ∼ l 1.44, and for an infinite inertial subrange, we find that K ∼ l 1.556-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 G K ≈ 0.73 and G l ≈ 0.01 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.