We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. With direct numerical simulations, we demonstrate that the rate of turbulent decay is governed by the reconnection of magnetic structures, and not necessarily 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 it does not constrain nonhelical 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 ${\text{volume}}^{1/2}$) magnetic helicity contained in any sufficiently large volume. We verify that this invariant is indeed well conserved in our numerical simulations. 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 nonhelical 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.

中文翻译：

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重联控制的磁流体动力学湍流衰减和不变量的作用

我们提出了在没有平均磁场的情况下磁主导的衰减湍流的新理论图。通过直接的数值模拟，我们证明了湍流衰减的速度是由磁结构的重新连接决定的，而不一定是由理想动力学决定的，正如之前假设的那样。我们通过提出湍流在重新连接时间尺度上衰减，同时尊重表示重新连接磁场满足的拓扑约束的某些积分不变量的守恒，从而获得对磁能衰减定律的预测。众所周知，磁螺旋度对于初始螺旋场配置是这样的不变量，但它不限制非螺旋衰减，其中体积平均磁螺旋密度消失。对于这样的衰败，${\text{体积}}^{1/2}$) 包含在任何足够大的体积中的磁性螺旋。我们验证了这个不变量在我们的数值模拟中确实很好守恒。我们的处理导致对磁能衰减定律的新预测：特别是，虽然我们期望规范${吨}^{-2/3}$ 重新连接快速时螺旋湍流的幂律（即等离子团主导或随机），我们发现一个更浅的 ${吨}^{-4/7}$在缓慢的“Sweet-Parker”重新连接机制中衰减，与现有的数值模拟更好地吻合。对于目前没有明确理论的非螺旋场，我们预测幂律${吨}^{-10/9}$ 和 ${吨}^{-20/17}$分别在快速和慢速重连机制中。我们制定了受类萨夫曼不变量守恒的湍流系统衰减的一般原理，并提出了如何将其应用于具有强平均磁场的 MHD 湍流和具有磁能和动能之间初始均分的各向同性 MHD 湍流。