小尺度turbulence快速随机畸变模型
A model for rapid stochastic distortions of small-scale turbulence
摘要：
我们提出了一个模型，描述小尺度的Navier-Stokes湍流的演变，由于其随机扭曲的大得多的湍流尺度。本研究的动机是数值研究结果（laval，2001），这种相互作用的分离尺度发挥重要作用的湍流不稳定性。我们介绍了湍流的k-空间量的矩的描述，使用以前开发的运动发电机问题（Nazarenko，2003）的方法。使用$k$ -空间矩允许引入新的有用的测量不连续性，例如平均偏振和光谱平坦度。对二维湍流的研究表明，能量级联是尺度不变的高斯型，而涡度拟能级联是间歇性的。在3D中，我们表明，湍流波包的统计偏离高斯对主导的平面偏振。这种湍流是由$k$空间中的椭球体形成的，椭球体以其原点为中心，具有一个大轴、一个中性轴和一个小轴，速度场平行于最小轴。
英文摘要：
We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of separated scales play important role in turbulence intermittency. We introduce description of turbulence in terms of the moments of the k-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko, 2003). Working with the $k$-space moments allows to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the 2D turbulence shows that the energy cascade is scale invariant and Gaussian whereas the enstrophy cascade is intermittent. In 3D, we show that the statistics of turbulence wavepackets deviates from gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centered at its origin and having one large, one neutral and one small axes with the velocity field pointing parallel to the smallest axis.
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