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arXiv 1611.04073physics.flu-dyn
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流体动力学和磁流体动力学turbulence中精确标度关系的另一种表述

An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence

Supratik Banerjee, Sebastien Galtier

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13 pages
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摘要：

我们提出了一个替代配方的精确关系，在三维均匀湍流使用两点统计。我们的发现说明与不可压缩流体动力学，标准和霍尔磁流体动力学湍流。在该公式中，湍流无粘不变量的级联率可以简单地用混合二阶结构函数表示。除速度${\bf u}$、涡量$ω$、磁场${\bf b}$和电流${\bf j}$等常用变量外，矢量${\bf u } \times {\boldsymbol ω}$、${\bf u} \times {\bf b}$和${\bf j} \times {\bf b}$也对湍流叶栅起着关键作用。目前的方法提供了一个简单的代数形式，这是特别有趣的研究各向异性的空间等离子体，如太阳风，在原则上更快的统计收敛比经典的法律写在三阶振荡器。

英文摘要：

We propose an alternative formulation for the exact relations in three-dimensional homogeneous turbulence using two-point statistics. Our finding is illustrated with incompressible hydrodynamic, standard and Hall magnetohydrodynamic turbulence. In this formulation, the cascade rate of an inviscid invariant of turbulence can be expressed simply in terms of mixed second-order structure functions. Besides the usual variables like the velocity ${\bf u}$, vorticity $ω$, magnetic field ${\bf b}$ and the current ${\bf j}$, the vectors ${\bf u } \times {\boldsymbol ω}$, ${\bf u} \times {\bf b}$ and ${\bf j} \times {\bf b}$ are also found to play a key role in the turbulent cascades. The current methodology offers a simple algebraic form which is specially interesting to study anisotropic space plasmas like the solar wind, with in principle a faster statistical convergence than the classical laws written in terms of third-order correlators.

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