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arXiv 1006.3549astro-ph.SR
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切变存在时的磁螺旋度通量

Magnetic helicity flux in the presence of shear

Alexander Hubbard, Axel Brandenburg

摘要:

磁螺旋度已经上升到发电机理论中的一个主要角色,小尺度场的螺旋度与大尺度场的发电机饱和过程有关。它是一个几乎守恒的量,这使得它的演化方程可以用产量和通量来表示。通量项可以用多种方式分解。Vishniac和Cho(2001,ApJ 550,752)分离出了一种特别的贡献,这种贡献被认为在平均切变存在的发电机中起着重要作用。然而,磁螺旋度通量明显依赖于规范,并且被称为Vishniac-Cho通量的相关性是在库仑规范中确定的,这在剪切系统中充满了复杂性。虽然小尺度螺旋度的通量是明确的规范相关,其发散可以是规范无关的。我们利用这一性质在剪切盒系统中通过直接数值模拟研究了小尺度场的磁螺旋度通量,发现在数值可用的规范下,小尺度场的磁螺旋度通量的发散消失,而Vishniac-Cho通量的发散保持有限。我们把这种看似矛盾的现象归因于小尺度磁螺旋度水平通量的存在,即使在我们的剪切周期域中也存在有限的发散。

英文摘要:

Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho (2001, ApJ 550, 752). Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems. While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite. We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences even in our shearing-periodic domain.

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