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 ) ∼ σ l ( 1 + p ) / 2; and for asymptotically infinite inertial subrange the simulations yield non-local regimes K ( l ) ∼ σ l γ, 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 ∼ σ l 1 . 556, in agreement with the revised 1926 dataset K ∼ σ l 1 . 564 [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.