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 e^I_K in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σ_l), such that e^I_K → 0 as σ_l/η → 1; and e^I_K → 1 as σ_l/η → 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σ_l/η < 1 in which the error e^I_K 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.