arXiv 1402.70582014-02-27physics.flu-dyncond-mat.stat-mechmath-phmath.MPphysics.comp-ph

二维均匀各向同性Turbulence中重粒子轨道内禀几何的统计性质

Statistical Properties of the Intrinsic Geometry of Heavy-particle Trajectories in Two-dimensional, Homogeneous, Isotropic Turbulence

Anupam Gupta, Dhrubaditya Mitra, Prasad Perlekar, Rahul Pandit

备注：: submitted to Phys. Rev. Lett. The supplementary information is added as an appendix

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摘要：

我们得到，通过广泛的直接数值模拟，在二维的，统计稳定的，均匀的，各向同性的湍流，摩擦的重惯性粒子的轨迹。我们表明，概率分布函数$\mathcal{P}(κ)$，轨迹曲率$κ$，是这样的，作为$κ\to \infty$，$\mathcal{P}(κ) \sim κ^{-h_{\rm r}}$，与$h_{\rm r} = 2.07 \pm 0.09$。指数$h_{\rm r}$是普适的，因为它与斯托克斯数（$\rm{St}$）和能量注入波数无关。我们表明，这个指数位于误差范围内的拉格朗日示踪剂的轨迹，他们的同行。我们证明了重粒子轨迹的复杂性可以通过轨迹中的拐点数$N_{\rm I}(t,{\rm St})$（直到时间$t$）和$n_{\rm I} ({\rm St}) \equiv \lim_{t\to\infty} \frac{N_{\rm I} (t,{\rm St})}{t} \sim {\rm St}^{-Δ}$来表征，其中指数$Δ= 0.33 \pm0.02$也是普适的。

英文摘要：

We obtain, by extensive direct numerical simulations, trajectories of heavy inertial particles in two-dimensional, statistically steady, homogeneous, and isotropic turbulent flows, with friction. We show that the probability distribution function $\mathcal{P}(κ)$, of the trajectory curvature $κ$, is such that, as $κ\to \infty$, $\mathcal{P}(κ) \sim κ^{-h_{\rm r}}$, with $h_{\rm r} = 2.07 \pm 0.09$. The exponent $h_{\rm r}$ is universal, insofar as it is independent of the Stokes number ($\rm{St}$) and the energy-injection wave number. We show that this exponent lies within error bars of their counterparts for trajectories of Lagrangian tracers. We demonstrate that the complexity of heavy-particle trajectories can be characterized by the number $N_{\rm I}(t,{\rm St})$ of inflection points (up until time $t$) in the trajectory and $n_{\rm I} ({\rm St}) \equiv \lim_{t\to\infty} \frac{N_{\rm I} (t,{\rm St})}{t} \sim {\rm St}^{-Δ}$, where the exponent $Δ= 0.33 \pm0.02$ is also universal.

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