Turbulent particle pair diffusion: Numerical simulations

A theory for turbulent particle pair diffusion in the inertial subrange [Malik NA, PLoS ONE 13(10):e0202940 (2018)] is investigated numerically using a Lagrangian diffusion model, Kinematic Simulations [Kraichnan RH, Phys. Fluids 13:22 (1970); Malik NA, PLoS ONE 12(12):e0189917 (2017)]. All predictions of the theory are observed in flow fields with generalised energy spectra of the type, E(k) ∼ k(−p). Most importantly, two non-Richardson regimes are observed: for short inertial subrange of size 10(2) the simulations yield quasi-local regimes for the pair diffusion coefficient, [Image: see text] ; and for asymptotically infinite inertial subrange the simulations yield non-local regimes [Image: see text] , with γ intermediate between the purely local scaling γ(l) = (1 + p)/2 and the purely non-local scaling γ(nl) = 2. For intermittent turbulence spectra, E(k) ∼ k(−1.72), the simulations yield [Image: see text] , in agreement with the revised 1926 dataset [Image: see text] [Richardson LF, Proc. Roy. Soc. Lond. A 100:709 (1926); Malik NA, PLoS ONE 13(10):e0202940 (2018)]. These results lend support to the physical picture proposed in the new theory that turbulent diffusion in the inertial subrange is governed by both local and non-local diffusion transport processes.