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

Abstract

Thomson, D. J. \& Devenish, B. J. [{\em 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. {\em J.~Fluid Mech.} 236, 281 (1992)], unreliable. Here it is shown 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 that the normalized integrated error $e^I_K$ in the turbulent pair diffusivity ($K$) due to the sweeping effect decreases with increasing pair separation ($\sigma_l$), such that $e^I_K\to 0$ as $\sigma_l/\eta\to \infty$; and $e^I_K\to \infty$ as $\sigma_l/\eta\to 0$. $\eta$ is the Kolmogorov turbulence microscale. There is an intermediate range of separations $1<\sigma_l/\eta< \infty$ 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, $1<\sigma_l/\eta< 10^5$, implying that the deviation from locality observed in KS therefore cannot be atributed to sweeping errors and could be real. This is important for pair diffusion theory and modeling.