论文标题
磁流体动力湍流的重新连接控制的衰减和不变的作用
Reconnection-controlled decay of magnetohydrodynamic turbulence and the role of invariants
论文作者
论文摘要
我们提出了在没有平均磁场的情况下磁性支配的新理论图片，腐烂的湍流。我们证明，这种湍流受磁结构的重新连接，而不是由理想动力学的重新连接，如先前所假定的那样。我们通过提出在重新连接时间标准上的湍流衰减来获得对磁能衰变定律的预测，同时尊重某些代表重新连接磁场满足的拓扑约束的某些积分不变的保存。众所周知，对于最初的螺旋场构型而言，磁性螺旋性是如此不变，但不限制非螺旋衰减，其中体积平均磁性密度消失了。对于这种衰变，我们提出了一个新的整体不变的，类似于流体动力湍流的Loitsyansky和Saffman不变式，表达了随机的保护（比例为$ \ MATHRM {losemrm {polumal}^{1/2} $），在任何足够的大容量中都包含在任何足够的大容量中。 Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker' reconnection regime, in better agreement with existing numerical simulations.对于目前没有确定性理论的非螺旋字段，我们分别预测$ t^{ - 10/9} $和$ t^{ - 20/17} $的权力定律，分别在快速和慢速连接方面。我们制定了湍流系统衰减的一般原理，受到saffman样不变性的保护，并提出如何使用强平均磁场将其应用于MHD湍流，并在磁性和动力学能量之间使用初始设备，并在磁性和动力学之间进行初始设备。
We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as $\mathrm{volume}^{1/2}$) magnetic helicity contained in any sufficiently large volume. Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker' reconnection regime, in better agreement with existing numerical simulations. For non-helical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.
