On two-dimensional magnetohydrodynamic turbulence
On two-dimensional magnetohydrodynamic turbulence
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关于二维磁流体动力湍流
DOI：
10.1017/s0022112078001950
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发表时间：
1978
影响因子：
3.7
通讯作者：
A. Pouquet
中科院分区：
文献类型：
--
作者：
A. Pouquet
结果表明，二维MHD湍流在某些方面更接近三维，而不是二维水动力湍流。二阶闭合表明：在零粘性和磁扩散时，奇点出现在有限时间；存在一个小尺度的能量级联和一个平方磁势的逆级联，这与Fyfe&Montgomery(1976)的猜想一致；小尺度的磁能在大尺度磁场上表现为负涡粘性；a(Iv)当注入磁能时，得到一个定态，对于正磁扩散系数λ，该定态具有零磁能(反发电机定理)；但是，在这个定态之前，有一个非常长的非零磁能平台，它可能扩展到λ→0的无限倍。结果表明，直接对高分辨率(5122或10242网格)的二维MHD方程进行数值模拟可以更好地理解充分发展的湍流的小尺度结构，特别是间歇性和几何问题。
It is shown that two-dimensional MHD turbulence is in certain respects closer to three-dimensional than to two-dimensional hydrodynamic turbulence. A second-order closure indicates that: at zero viscosity and magnetic diffusivity, a singularity appears at a finite time; there is an energy cascade to small scales and an inverse cascade of squared magnetic potential, in agreement with a conjecture of Fyfe & Montgomery (1976); small-scale magnetic energy acts like a negative eddy viscosity on large-scale magnetic fields;a (iv) upon injection of magnetic energy, a stationary state is obtained which has zero magnetic energy for a positive magnetic diffusivity λ (anti-dynamo theorem); however, this stationary state is preceded by a very long non-zero magnetic energy plateau which probably extends to infinite times as λ → 0. It is suggested that direct numerical simulation of the two-dimensional MHD equations with high resolution (a 5122 or 10242 grid) could lead to a better understanding of the small-scale structure of fully developed turbulence, especially questions of intermittency and geometry.