Title: In search of random uncorrelated particle motion (RUM) in a simple random flow field Show Chinese title

Title: 寻找简单随机流场中的随机不相关粒子运动（RUM）

Abstract: DNS studies of dispersed particle motion in isotropic homogeneous turbulence [1] have revealed the existence of a component of random uncorrelated motion (RUM)dependent on the particle inertia {\tau}p(normalised particle response time or Stoke number). This paper reports the presence of RUM in a simple linear random smoothly varying flow field of counter rotating vortices where the two-particle velocity correlation was measured as a function of spatial separation. Values of the correlation less than one for zero separation indicated the presence of RUM. In terms of Stokes number, the motion of the particles in one direction corresponds to either a heavily damped ({\tau}p < 0.25) or lightly damped ({\tau}p > 0.25)harmonic oscillator. In the lightly damped case the particles overshoot the stagnation lines of the flow and are projected from one vortex to another (the so-called sling-shot effect). It is shown that RUM occurs only when {\tau}p > 0.25, increasing monotonically with increasing Stokes number. Calculations of the particle pair separation distribution function show that equilibrium of the particle concentration field is never reached, the concentration at zero separation increasing monotonically with time. This is consistent with the calculated negative values of the average Liapounov exponent (finite compressibility) of the particle velocity field. Show Chinese abstract

Abstract: DNS研究显示，在各向同性均匀湍流中分散粒子的运动存在一个与粒子惯性{\tau }p（归一化粒子响应时间或斯托克斯数）相关的随机不相关运动（RUM）成分。本文报告了在由反向旋转涡旋组成的简单线性随机平滑变化流场中存在RUM，其中测量了两粒子速度相关性随空间分离的变化情况。零分离时的相关值小于1表明存在RUM。就斯托克斯数而言，粒子在一个方向上的运动对应于重阻尼（{\tau }p < 0.25）或轻阻尼（{\tau }p > 0.25）谐振子。在轻阻尼情况下，粒子会超过流场的停滞线，并从一个涡旋被投射到另一个涡旋（所谓的弹弓效应）。结果表明，只有当{\tau }p > 0.25时才会出现RUM，并且随着斯托克斯数的增加而单调增加。粒子对分离分布函数的计算表明，粒子浓度场从未达到平衡，零分离处的浓度随时间单调增加。这与计算得到的粒子速度场的平均李雅普诺夫指数为负值（有限压缩性）是一致的。