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 102 the simulations yield quasi-local regimes for the pair diffusion coefficient, K(l) ∼ s(1+p)=2 l ; and for asymptotically infinite inertial subrange the simulations yield non-local regimes K(l) ∼ sg l , with γ intermediate between the purely local scaling γl = (1 + p)/2 and the purely non-local scaling γnl = 2. For intermittent turbulence spectra, E(k) ∼ k-1.72, the simulations yield K ∼ σ1:556 l , in agreement with the revised 1926 dataset K ∼ σ1:564 l [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.