Turbulence中晶粒聚集的一个简单唯象模型
A Simple Phenomenological Model for Grain Clustering in Turbulence
摘要：
我们提出了一个简单的模型的密度波动的气动颗粒，嵌入在一个湍流，重力气体盘。该模型结合了一组颗粒遇到一个单一的湍流涡的行为的计算，与涡的统计的分层近似。这使得分析预测的范围内的数量，包括：分布的晶粒密度，功率谱和关联函数的波动，并达到最大晶粒密度。我们预测这些尺度如何作为一个函数的晶粒拖动时间t_stop，空间尺度，颗粒与气体的质量比，湍流强度（α），和详细的磁盘属性。我们测试这些对数值模拟与各种连续性驱动机制。模拟结果与预测吻合良好，跨度t_stop*Omega ~ 1 e-4 - 10，alpha ~ 1 e-10 - 1 e-2，颗粒与气体质量比~0-3。从“湍流浓度”模拟和实验室实验的结果也预测作为一个特例。大范围尺度的涡旋分等级地分散和集中颗粒。对于小颗粒，这是最有效的涡流周转时间可比的停止时间，但波动也阻尼本地气体颗粒漂移。对于大颗粒，剪切和重力导致更广泛的涡旋尺度驱动波动，最大的功率在最大的尺度上。颗粒密度分布具有对数泊松形状，对于大颗粒具有高达因子>1000的波动。我们提供了简单的分析表达式的预测，并讨论了星子形成，晶粒生长和湍流结构的影响。
英文摘要：
We propose a simple model for density fluctuations of aerodynamic grains, embedded in a turbulent, gravitating gas disk. The model combines a calculation for the behavior of a group of grains encountering a single turbulent eddy, with a hierarchical approximation of the eddy statistics. This makes analytic predictions for a range of quantities including: distributions of grain densities, power spectra and correlation functions of fluctuations, and maximum grain densities reached. We predict how these scale as a function of grain drag time t_stop, spatial scale, grain-to-gas mass ratio, strength of turbulence (alpha), and detailed disk properties. We test these against numerical simulations with various turbulence-driving mechanisms. The simulations agree well with the predictions, spanning t_stop*Omega ~ 1e-4 - 10, alpha ~ 1e-10 - 1e-2, and grain-to-gas mass ratio ~0-3. Results from 'turbulent concentration' simulations and laboratory experiments are also predicted as a special case. Vortices on a wide range of scales disperse and concentrate grains hierarchically. For small grains this is most efficient in eddies with turnover time comparable to the stopping time, but fluctuations are also damped by local gas-grain drift. For large grains, shear and gravity lead to a much broader range of eddy scales driving fluctuations, with most power on the largest scales. The grain density distribution has a log-Poisson shape, with fluctuations for large grains up to factors >1000. We provide simple analytic expressions for the predictions, and discuss implications for planetesimal formation, grain growth, and the structure of turbulence.
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