Velocity statistics for point vortices in the local α-models of turbulence
Velocity statistics for point vortices in the local α-models of turbulence
复制标题
湍流局部 α 模型中点涡的速度统计
DOI：
10.1080/03091929.2019.1572750
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发表时间：
2019
影响因子：
1.3
通讯作者：
G. Badin
中科院分区：
文献类型：
--
作者：
G. Conti;G. Badin
本文研究了α湍流方程中点涡模型的速度脉动，其特征是活动标量与流函数之间的分数拉普拉斯关系。特别是，我们专注于本地动态政权。局部动力学不同于研究充分的2D湍流的情况，因为它允许考虑真正的热力学极限，也就是说，考虑在无限平面上的无限组点涡，保持涡的密度恒定。这一限制的结果是，所获得的结果是独立的系统中的点涡的数量。未为2D湍流定义此限制。我们显示了不同程度的本地化的速度波动的概率密度分布的分析形式。分布的中心区域不是高斯分布，与湍流的情况相反，但在小速度限制下可以近似为高斯函数。分布的尾部表现出幂律行为和自相似性的密度变量。由于热力学的限制，核心的高斯近似和尾部的陡度都与点涡的数目无关，而依赖于α模型。在经典湍流α模型的背景下，我们还证明了均匀分布点涡的速度统计与非均匀分布点涡的速度统计之间的联系。由于幂律的指数仅取决于α，我们通过模拟不同α值的全湍流场来检验用点涡近似得到的幂律近似，并计算速度场绝对值的相应概率密度分布。这些结果表明，在海洋或大气中的湍流波动的局部性质可能会推导出的概率密度函数的尾部的形状。
The velocity fluctuations for point vortex models are studied for theα-turbulence equations, which are characterised by a fractional Laplacian relation between active scalar and the streamfunction. In particular, we focus on the local dynamics regime. The local dynamics differ from the well-studied case of 2D turbulence as it allows to consider the true thermodynamic limit, that is, to consider an infinite set of point vortices on an infinite plane keeping the density of the vortices constant. The consequence of this limit is that the results obtained are independent on the number of point vortices in the system. This limit is not defined for 2D turbulence. We show an analytical form of the probability density distribution of the velocity fluctuations for different degrees of locality. The central region of the distribution is not Gaussian, in contrast to the case ofturbulence, but can be approximated with a Gaussian function in the small velocity limit. The tails of the distribution exhibit a power law behaviour and self similarity in terms of the density variable. Due to the thermodynamic limit, both the Gaussian approximation for the core and the steepness of the tails are independent on the number of point vortices, but depend on theα-model. We also show the connection between the velocity statistics for point vortices uniformly distributed, in the context of theα-model in classical turbulence, with the velocity statistics for point vortices non-uniformly distributed. Since the exponent of the power law depends just onα, we test the power law approximation obtained with the point vortex approximation, by simulating full turbulent fields for different values ofαand we compute the correspondent probability density distribution for the absolute value of the velocity field. These results suggest that the local nature of the turbulent fluctuations in the ocean or in the atmosphere might be deduced from the shape of the tails of the probability density functions.
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影响因子：
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DOI：
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发表时间：
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期刊：
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影响因子：
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作者：
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通讯作者：
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