Effect of gravity on clustering patterns and inertial particle attractors in kinematic simulations

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)∼σl(1+p)/2; and for asymptotically infinite inertial subrange the simulations yield non-local regimes K(l)∼σlγ, 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 K∼σl1.556, in agreement with the revised 1926 dataset K∼σl1.564 [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.

Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model

Thomson, D. J. & Devenish, B. J. [J. Fluid Mech. 526, 277 (2005)] and others have suggested that sweeping effects make Lagrangian properties in Kinematic Simulations (KS), Fung et al [Fung J. C. H., Hunt J. C. R., Malik N. A. & Perkins R. J. J. Fluid Mech. 236, 281 (1992)], unreliable. However, such a conclusion can only be drawn under the assumption of locality. The major aim here is to quantify the sweeping errors in KS without assuming locality. Through a novel analysis based upon analysing pairs of particle trajectories in a frame of reference moving with the large energy containing scales of motion it is shown that the normalized integrated error eKI in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σ_l), such that eKI→0 as σ_l/η → ∞; and eKI→∞ as σ_l/η → 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σ_l/η < ∞ in which the error eKI remains negligible. Simulations using KS shows that in the swept frame of reference, this intermediate range is large covering almost the entire inertial subrange simulated, 1 < σ_l/η < 10⁵, implying that the deviation from locality observed in KS cannot be atributed to sweeping errors. This is important for pair diffusion theory and modeling. PACS numbers: 47.27.E?, 47.27.Gs, 47.27.jv, 47.27.Ak, 47.27.tb, 47.27.eb, 47.11.-j.

Effect of the energy-spectrum law on clustering patterns for inertial particles subjected to gravity in kinematic simulation

We study the clustering of inertial particles using a periodic kinematic simulation. Particle clustering is observed for different pairs of Stokes number and Froude number and different spectral power laws (1.4≤p≤2.1). The main focus is to identify and then quantify the effect of p on the clustering attractor-by attractor we mean the set of points in the physical space where the particles settle when time tends to infinity. It is observed that spectral power laws can have a dramatic effect on the attractor shape. In particular, we observed an attractor type which was not present in previous studies for Kolmogorov spectra (p=5/3).