A Comparison between Markovian and Non-Markovian Closures in Simulations of Nonlinear Dynamos with Application to the Protogalactic Dynamo
A Comparison between Markovian and Non-Markovian Closures in Simulations of Nonlinear Dynamos with Application to the Protogalactic Dynamo
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非线性发电机模拟中马尔可夫闭包与非马尔可夫闭包的比较及其在原银河发电机中的应用
DOI：
10.1086/304413
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
B. Chandran
中科院分区：
文献类型：
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作者：
B. Chandran
非螺旋磁流体动力学（MHD）湍流和非线性发电机的数值研究使用两个统计封闭：直接相互作用近似，或DIA（Kraichnan），和可实现的马尔可夫封闭，或RMC（鲍曼等人）。RMC是DIA的近似版本，可用于模拟更长时间内更宽范围的波数。在一个受控的数值实验中，它被发现，DIA和RMC导致可比的非线性发电机的模拟结果。这有助于证明RMC和其他马尔可夫闭包在发电机问题中的使用，从而支持了Pouquet，Frisch和Léorat的结果，即初始弱磁场在所有尺度上都增长到动能的大致均分。Pouquet、Frisch和Léorat得到的结果也可直接通过DIA数值计算得到。一个单独的DIA计算产生的k-3/2谱的稳态各向同性MHD湍流，在雅阁的物理参数Kraichnan。一个粗略的初步计算的基础上的RMC表明，在Kulsrud等人的理论中的原星系的崩溃过程中的磁能增长到约6%的动能。在技术方面，几何算法计算波数仓体积因子在三维封闭计算。
Nonhelical magnetohydrodynamic (MHD) turbulence and the nonlinear dynamo are investigated numerically using two statistical closures: the direct interaction approximation, or DIA (Kraichnan), and the realizable Markovian closure, or RMC (Bowman et al.). The RMC is an approximate version of the DIA that can be used to simulate wider ranges of wavenumbers for longer stretches of time. In a controlled numerical experiment, it is found that the DIA and RMC lead to comparable results in simulations of the nonlinear dynamo. This helps justify the use of the RMC and other Markovian closures for the dynamo problem, thereby supporting the result of Pouquet, Frisch, & Léorat that an initially weak magnetic field grows up to rough equipartition with the kinetic energy on all scales. The result obtained by Pouquet, Frisch, & Léorat is also reproduced directly with a numerical DIA calculation. A separate DIA calculation produces k-3/2 spectra for steady state isotropic MHD turbulence, in accord with the physical arguments of Kraichnan. A rough preliminary calculation based upon the RMC suggests that the magnetic energy grows to approximately 6% of the kinetic energy during the collapse of the protogalaxy in the theory of Kulsrud et al. In a technical aside, a geometric algorithm is presented for calculating wavenumber-bin volume factors in three-dimensional closure calculations.