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arXiv 1609.02601physics.flu-dyn
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在湍流中,颗粒在旋涡区停留多长时间?

How long do particles spend in vortical regions in turbulent flows?

Akshay Bhatnagar, Anupam Gupta, Dhrubaditya Mitra, Rahul Pandit, Prasad Perlekar

摘要:

通过对统计稳定、均匀、各向同性湍流平流作用下的拉格朗日示踪粒子或重惯性粒子在三维不可压纳维-斯托克斯方程中的直接数值模拟,得到了它们在湍流涡旋区或应变主导区所处时间的概率分布函数.我们使用的两个不变量,$Q$和$R$,速度梯度张量来区分涡流和应变为主的区域的流动和分区的$Q-R$平面分为四个不同的区域取决于拓扑结构的流动,这四个区域中的两个对应于涡流为主的流动区域和两个对应于应变为主的。我们得到了沿示踪粒子和重惯性粒子轨迹的$Q$和$R$,并找出了它们在$Q-R$平面的四个区域之一中停留的时间$\mathrm{t_{pers}}$。我们发现,$\mathrm{t_{pers}}$的PDF显示指数衰减的尾巴为所有四个区域的示踪剂和重惯性粒子。从这些PDF中,我们提取特征时间尺度,这有助于我们量化这些颗粒在涡流或应变主导的流动区域中所花费的时间。

英文摘要:

We obtain the probability distribution functions (PDFs) of the time that a Lagrangian tracer or a heavy inertial particle spends in vortical or strain-dominated regions of a turbulent flow, by carrying out direct numerical simulation (DNS) of such particles advected by statistically steady, homogeneous and isotropic turbulence in the forced, three-dimensional, incompressible Navier-Stokes equation. We use the two invariants, $Q$ and $R$, of the velocity-gradient tensor to distinguish between vortical and strain-dominated regions of the flow and partition the $Q-R$ plane into four different regions depending on the topology of the flow; out of these four regions two correspond to vorticity-dominated regions of the flow and two correspond to strain-dominated ones. We obtain $Q$ and $R$ along the trajectories of tracers and heavy inertial particles and find out the time $\mathrm{t_{pers}}$ for which they remain in one of the four regions of the $Q-R$ plane. We find that the PDFs of $\mathrm{t_{pers}}$ display exponentially decaying tails for all four regions for tracers and heavy inertial particles. From these PDFs we extract characteristic times scales, which help us to quantify the time that such particles spend in vortical or strain-dominated regions of the flow.

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