Two-particle dispersion in turbulentlike flows
Two-particle dispersion in turbulentlike flows
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DOI：
10.1103/physreve.57.1677
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发表时间：
1998-02
影响因子：
2.4
通讯作者：
J. Fung;J. C. Vassilicos
中科院分区：
文献类型：
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作者：
J. Fung;J. C. Vassilicos
拉格朗日平均浓度计算需要单粒子统计知识。然而，如果拉格朗浓度波动和浓度协方差的计算要考虑与相对色散相关的湍流混合，那么这种计算必须包含两粒子静态的一些特征和性质@1#。浓度协方差的计算对于化学反应和大气中的反应速率的预测是重要的，因为化学反应速率取决于浓度协方差而不是平均浓度。浓度波动的计算对空气质量控制、燃烧和地球物理流动中的污染物扩散也很重要。也许是双粒子d粒子最重要的统计数据，当然也是最常被研究的！是两个流体元之间的均方距离~在本文中称为粒子！D(t)，它当然是时间t的函数。在某些情况下，例如线性浓度梯度@1#的下行压力，D(t)是计算浓度通量所需的唯一双粒子统计量。一般来说，D(t)是湍流色散理论中重要的基本量之一。在1926年开始的一系列论文中，理查德森@2#研究了湍流扩散系数（d/dt） d (t)作为大气湍流平流的两个粒子之间距离d的函数。（d/dt） d；(D)，暗示D；t ~忽略粒子对之间的初始距离，假设D0 ！D2在一个足够大的时间！Obukhov @3#和Batchelor@4#将Ko mogorov的相似性参数应用于D(t)，从理论上推导出Richardson的色散定律，得到D(t)；在中间惯性范围内的Et乘以t ~e是每单位质量流体的平均耗散率！当时间尺度远大于相关积分时间尺度D(t)时；T，因为两个粒子分开独立运动
Lagrangian calculations of average concentrations req knowledge of one-particle statistics. However, if Lagrang calculations of concentration fluctuations and concentra covariances are to account for turbulent mixing associa with relative dispersion, then such calculations must inc porate some features and properties of two-particle statis @1#. The calculation of concentration covariances is imp tant in the prediction of reaction rates in chemical react and in the atmosphere because chemical reaction rates pend on concentration covariances and not on average centrations. The calculation of concentration fluctuations also important for air-quality control, combustion, and p lutant dispersal in geophysical flows. Perhaps the most important statistic of two-particle d persion~certainly the most frequently studied ! is the mean square distance between two fluid elements ~al o referred to as particles in this paper !, D(t), which is of course a function of time t. In certain circumstances, such as downstre of a linear concentration gradient @1#, D(t) is the only twoparticle statistic needed to calculate concentration fluc tions. In general, D(t) is one of the fundamental quantitie of interest in the theory of turbulent dispersion. In a series papers starting in 1926, Richardson @2# studied the turbulen diffusivity (d/dt)D(t) as a function of the distance D between two particles advected by atmospheric turbulence. chardson’s empirical finding, ( d/dt)D;(D), implies D;t ~neglecting the initial distanceD0 between pairs of particles under the assumption that D0 !D2 at a timet that is sufficiently large!. Obukhov @3# and Batchelor@4# derived Richardson’s dispersion law theoretically by applying Ko mogorov’s similarity arguments toD(t) and obtained D(t);et in an intermediate inertial range of times t ~e is the average rate of dissipation per unit mass of fluid !. When the timet is much larger than correlation integral time scal D(t);t because the two particles move apart independe