Presence of a Richardson's regime in kinematic simulations

In this paper we investigate kinematic simulation (KS) consistency with the theory of Richardson [Proc. Roy. Soc. A 110, 24 (1926)] for two-particle diffusivity. In particular we revisit the sweeping problem. It has been argued by Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).] that due to the lack of sweeping of small scales by large scales in kinematic simulation, the validity of Richardson's power law might be affected. Here, we argue that the discrepancies between authors on the ability of kinematic simulation to predict Richardson power law may be linked to the inertial subrange they have used. For small inertial subranges, KS is efficient and the significance of the sweeping can be ignored, as a result we limit the KS agreement with the Richardson scaling law t(3) for inertial subranges k(N0/k(1)≤10000. For larger inertial range KS does not fully follow the t(3) law. Unfortunately, there is no experimental data to compare KS with and draw conclusions for such large inertial subranges. It cannot be concluded either that the discrepancy between KS and Richardson's theory for larger inertial subranges is exactly taken into account by the theory developed in Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).].