Khan M A I, Pumir A, Vassilicos J C
DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 2):026313. doi: 10.1103/PhysRevE.68.026313. Epub 2003 Aug 26.
As three particles are advected by a turbulent flow, they separate from each other and develop nontrivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in two dimensions, by kinematic simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first demonstrate that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at a much higher Reynolds number is then considered. The numerical results support the existence of nontrivial shape statistics, with a high probability of having elongated triangles. Even at the highest available inertial range of scales, corresponding to a ratio between large and small scale L/eta=17,000, a perfect self-similar regime is not found. The effects of the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results, are also discussed. Special attention is given to the effects of persistence of spatial flow structure.
当三个粒子被湍流平流输送时，它们彼此分离并形成复杂的几何形状，这有效地反映了湍流的结构。在此，我们从统计学角度研究二维运动学模拟（KS）中三个拉格朗日粒子平流输送的几何形状。KS是一种湍流扩散的拉格朗日模型，在任何层面都不使用任何时间上的δ相关性。通过这种方法，可以研究具有非常大范围的惯性尺度和不同空间流动结构持续性的情况。我们首先证明该模型流在低雷诺数下再现了最近的实验结果。然后考虑了在高得多的雷诺数下形状分布的统计特性。数值结果支持了复杂形状统计的存在，即出现细长三角形的概率很高。即使在最高可用的惯性尺度范围内，对应于大尺度与小尺度之比L/η = 17,000，也未发现完美的自相似 regime。还讨论了合成流参数的影响，例如频谱指数和扫掠效应如何影响我们的结果。特别关注空间流动结构持续性的影响。
