Growth of turbulent magnetic fields.
Growth of turbulent magnetic fields.
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湍流磁场的增长。
DOI：
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
S. Nagarajan
中科院分区：
文献类型：
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作者：
R. Kraichnan;S. Nagarajan
借助于磁能谱初始增长的精确表达式，讨论了高导电各向同性湍流流体中弱随机初始磁场的演化。等分论点、涡度类比和已知的湍流近似都不足以预测磁能最终是消亡还是指数增长。对于磁扩散率λ与运动粘度ν的任何比率都是如此。因此，最终增长和最终衰变的可能性都是被承认的，并且，对于每一种可能性，通过简单的动力学论证来估计λ？ν情况下的磁能谱的形状。如果存在增长，则可以得出结论：在欧姆截止点以下的磁谱最终与动能谱达到均分，大致类似于比尔曼和施鲁特所预言的方式，但主要的例外是等分惯性范围内的动能谱演化成k−3/2形式，并且通过欧姆耗散范围的一部分保持均分，谱迅速下降。用拉格朗日历史直接相互作用方程提出的简化转移近似，数值计算了弱场λ？ν区的磁谱演化。这一计算结果最终得出磁能的指数增长非常微弱。
The evolution of a weak, random initial magnetic field in a highly conducting, isotropically turbulent fluid is discussed with the aid of the exact expression for initial growth of the magnetic energy spectrum. Equipartition arguments, the vorticity analogy, and the known turbulence approximations all are found inadequate for predicting whether the magnetic energy eventually dies away or grows exponentially. This is true for any ratio of magnetic diffusivity λ to kinematic viscosity ν. The possibilities of eventual growth and eventual decay are therefore both admitted, and, for each, the shape of the magnetic‐energy spectrum in the case λ » ν is estimated by simple dynamical arguments. If there is growth, it is concluded that the magnetic spectrum below the Ohmic cut‐off eventually reaches equipartition with the kinetic‐energy spectrum roughly in the fashion predicted by Biermann and Schluter, with the principal exceptions that the spectrum of kinetic energy in the equipartition inertial range evolves to the form k −3/2 and that equipartition is maintained, with rapidly falling spectrum, through part of the Ohmic dissipation range. The evolution of the magnetic spectrum in the weak‐field λ » ν regime is also computed numerically with a simplified transfer approximation suggested by the Lagrangian‐history direct‐interaction equations. This calculation turns out to yield an eventual very weak exponential growth of magnetic energy.