论文标题
概率密度在均质和各向同性磁流动力湍流中的功能
Probability Density Functions in Homogeneous and Isotropic Magneto-Hydrodynamic Turbulence
论文作者
论文摘要
我们得出了磁溶解动力（MHD）湍流中多点概率密度函数的进化方程的层次结构。我们讨论了Chandrasekhar得出的MHD湍流的层次结构的关系，并为关节特征功能提供了功能方程，该方程可被视为与HOPF功能在流体动力湍流中的类似物。此外，我们为单点磁场概率密度函数的进化方程开发了一种闭合方法，该方法基于未闭合项的关节高斯假设。明确表明，这种封闭以及均匀性和各向同性的假设导致非线性术语消失。我们讨论了这一发现对磁场产生的含义，并简要介绍了包括平均磁场的轴对称理论。
We derive a hierarchy of evolution equations for multi-point probability density functions in magneto-hydrodynamic (MHD) turbulence. We discuss the relation to the moment hierarchy in MHD turbulence derived by Chandrasekhar and derive a functional equation for a joint characteristic functional which can be considered as the analogon to the Hopf functional in hydrodynamic turbulence. Furthermore, we develop a closure method for the evolution equation of the single-point magnetic field probability density function which is based on a joint Gaussian assumption for unclosed terms. It is explicitly shown that this closure, together with the assumptions of homogeneity and isotropy, leads to vanishing nonlinear terms. We discuss the implications of this finding for magnetic field generation and give a brief outlook on an axisymmetric theory which includes a mean magnetic field.
