Nonlocality and intermittency in three-dimensional turbulence
Nonlocality and intermittency in three-dimensional turbulence
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DOI：
10.1063/1.1373686
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发表时间：
2001-07-01
影响因子：
4.6
通讯作者：
Nazarenko, S
中科院分区：
文献类型：
--
作者：
Laval, JP;Dubrulle, B;Nazarenko, S
数值模拟被用来确定的非局部和局部相互作用的影响，在三维湍流的标度特性的不稳定性修正。我们发现，忽略局部相互作用会导致小尺度能谱增强，并导致大量非常强烈的涡旋（“龙卷风”）和更强的不稳定性（例如，速度增量的概率分布函数中较宽的尾部和较大的异常校正）。另一方面，忽略非定域相互作用导致更强的小尺度谱，但显着较弱的非定域性。因此，不稳定性的大小并不仅仅取决于小尺度的平均强度，而是由尺度相互作用的性质决定的。也就是说，非局部相互作用的作用是产生强烈的旋涡，负责不稳定性和局部相互作用的作用是消散它们。基于这些观察，提出了一种新的湍流模型，其中非局部（类似快速畸变理论）相互作用通过具有加性噪声的乘法过程耦合大尺度和小尺度，湍流粘性模型模拟局部相互作用。这个模型是用来推导一个简单的版本的朗之万方程的小规模的速度增量。高斯近似的大尺度场产生的速度增量的概率分布函数的福克-普朗克方程。该方程的稳态解可以定性地解释反常修正和沿着尺度的偏态产生。一个至关重要的作用是由加法和乘法（大尺度）过程之间的相关性，拉伸和涡度之间的相关性为特征。(C)2001年美国物理学会。
Numerical simulations are used to determine the influence of the nonlocal and local interactions on the intermittency corrections in the scaling properties of three-dimensional turbulence. We show that neglect of local interactions leads to an enhanced small-scale energy spectrum and to a significantly larger number of very intense vortices ("tornadoes") and stronger intermittency (e.g., wider tails in the probability distribution functions of velocity increments and greater anomalous corrections). On the other hand, neglect of the nonlocal interactions results in even stronger small-scale spectrum but significantly weaker intermittency. Thus, the amount of intermittency is not determined just by the mean intensity of the small scales, but it is nontrivially shaped by the nature of the scale interactions. Namely, the role of the nonlocal interactions is to generate intense vortices responsible for intermittency and the role of the local interactions is to dissipate them. Based on these observations, a new model of turbulence is proposed, in which nonlocal (rapid distortion theory-like) interactions couple large and small scale via a multiplicative process with additive noise and a turbulent viscosity models the local interactions. This model is used to derive a simple version of the Langevin equations for small-scale velocity increments. A Gaussian approximation for the large scale fields yields the Fokker-Planck equation for the probability distribution function of the velocity increments. Steady state solutions of this equation allows one to qualitatively explain the anomalous corrections and the skewness generation along scale. A crucial role is played by the correlation between the additive and the multiplicative (large-scale) process, featuring the correlation between the stretching and the vorticity. (C) 2001 American Institute of Physics.