Nicolleau F C G A, Nowakowski A F
Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056317. doi: 10.1103/PhysRevE.83.056317. Epub 2011 May 16.
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).].
在本文中，我们研究了运动学模拟（KS）与理查森理论[《皇家学会学报》A辑110, 24 (1926)]在双粒子扩散率方面的一致性。特别地，我们重新审视了扫掠问题。汤姆森和德文什[《流体力学杂志》526, 277 (2005)]认为，由于运动学模拟中缺乏大尺度对小尺度的扫掠，理查森幂律的有效性可能会受到影响。在此，我们认为作者们在运动学模拟预测理查森幂律能力上的差异可能与他们所使用的惯性子范围有关。对于小惯性子范围，运动学模拟是有效的，扫掠的影响可以忽略不计，因此我们将运动学模拟与理查森标度律t(3)的一致性限制在惯性子范围k(N0/k(1)≤10000。对于较大的惯性范围，运动学模拟并不完全遵循t(3)定律。不幸的是，没有实验数据可用于与运动学模拟进行比较并针对如此大的惯性子范围得出结论。也不能得出结论说，汤姆森和德文什[《流体力学杂志》526, 277 (2005)]所发展的理论恰好考虑到了运动学模拟与理查森理论在较大惯性子范围上的差异。
