分层磁旋转turbulence中场型传播的平均场方法
A mean-field approach to the propagation of field patterns in stratified magneto rotational turbulence
摘要：
分层磁旋转湍流的局部剪切盒模拟总是表现出周期性的场模式，传播远离磁盘中平面。一个常见的解释是磁浮力。然而，Shi等人最近的分析表明，在一个圆盘尺度高度H以下，流动是非常稳定的，因此需要在该区域进行另一种解释。在这里，我们进行和分析直接数值模拟来解释所观察到的行为的平均场描述。除了平均径向和方位场，我们监测小尺度电流螺旋度，我们建议作为一个关键指标的饱和。重建水平平均场，我们证明了问题可以减少到一个一维感应方程。通过所谓的测试场方法，我们然后确定基本的封闭参数。我们的分析表明，除了一个可能的直接MRI发电机，两个不同的间接发电机机制在椎间盘中运作。这解决了MRI发电机效应的“错误”信号的问题。最后，我们使用得到的封闭参数运行一个动态淬火发电机模型。该模型近似地恢复了在平均场中观察到的场模式。此外，该模式再现了占主导地位的宇称和独特的相位图案的小尺度电流螺旋度。后者的性质可能会打开一个潜在的路线，以了解磁共振成像诱导湍流的饱和。
英文摘要：
Local shearing box simulations of stratified magneto rotational turbulence invariably exhibit cyclic field patterns which propagate away from the disc midplane. A common explanation for this is magnetic buoyancy. The recent analysis by Shi et al. however shows that the flow is buoyantly stable below one disc scale height H, necessitating an alternative explanation in this region. We here conduct and analyse direct numerical simulations to explain the observed behaviour by means of a mean-field description. Apart from the mean radial and azimuthal field, we monitor the small-scale current helicity, which we propose as a key indicator for saturation. Reconstructing the horizontally averaged field, we demonstrate that the problem can be reduced to a one-dimensional induction equation. By means of the so-called test field method, we then determine the underlying closure parameters. Our analysis shows that, apart from a possible direct MRI dynamo, two distinct indirect dynamo mechanisms operate in the disc. This resolves the issue of the "wrong" sign of the MRI dynamo effect. Finally, we use the obtained closure parameters to run a dynamically quenched dynamo model. This model approximately recovers the observed field patterns in the mean fields. Moreover, the model reproduces the prevailing parity and the distinct phase pattern in the small-scale current helicity. The latter property might open a potential route to understand the saturation of MRI induced turbulence.
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