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

TL;DR

This paper demonstrates that sweeping effects in turbulent pair diffusion decrease with increasing particle separation, suggesting that observed deviations from locality in Kinematic Simulations are not due to sweeping errors, thus supporting their validity.

Contribution

It introduces a novel analysis method showing sweeping errors diminish at larger separations, challenging previous assumptions about their impact on Lagrangian turbulence models.

Findings

Error in turbulent pair diffusivity decreases with separation

Sweeping effects are negligible in the inertial subrange

Deviations from locality are likely genuine, not due to sweeping errors

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.