中的Craig XY分布与拉格朗日幂统计量 二维湍流

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摘要翻译：
本文在拉格朗日框架下研究了定常二维湍流数值模拟中能量注入率（功率）的概率分布函数(pdf)。该模拟是为了模拟电磁驱动的流体层，这是一个在实验室中产生二维湍流的有文献记载的系统。在我们的模拟中，强迫场和速度场都接近高斯分布。另一方面，测量到的注入功率的PDF在零处急剧地达到峰值，暗示那里有一个奇点，尾巴是指数的但不对称的。大的正波动比大的负波动更有可能。正是这种尾巴的不对称，导致能量输入的净平均值为正，尽管最有可能的值为零。对于两个相关正态变量乘积的PDF，Craig的XY分布很好地描述了功率分布的主要特征。我们证明了幂分布在零点处呈现对数奇异性，当幂的绝对值较大时，幂分布呈指数衰减。我们计算了渐近性态，并用力和速度的相关系数来表示尾部的不对称性。我们将测量的pdf与理论计算进行了比较，并简要讨论了功率pdf随其他强迫机制的变化。
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英文标题：
《Craig's XY-distribution and the statistics of Lagrangian power in
  two-dimensional turbulence》
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作者：
M. Bandi and C. Connaughton
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We examine the probability distribution function (pdf) of energy injection rate (power) in numerical simulations of stationary two--dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating two--dimensional turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails, which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured pdfs with the theoretical calculations and briefly discuss how the power pdf might change with other forcing mechanisms.
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PDF链接：
https://arxiv.org/pdf/710.1133

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关键词：Craig 拉格朗日 拉格朗 AIG 统计量 Craig dimensional 测量 pdf simulations