Spatial scales and locality of magnetic helicity
Spatial scales and locality of magnetic helicity
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DOI：
10.1051/0004-6361/201936675
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发表时间：
2019-09
影响因子：
6.5
通讯作者：
C. Prior;G. Hawkes;M. Berger
中科院分区：
文献类型：
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作者：
C. Prior;G. Hawkes;M. Berger
上下文在电阻磁流体力学模型中，磁螺旋度近似守恒。它量化了等离子体中磁场的纠缠。螺旋度的输运和消除对太阳内部发电机的发展和日冕活动区的演化都是至关重要的。这种传输通常导致高度不均匀的纠缠分布。目标。在不同的空间尺度和局部区域，没有一致的系统方法来分解螺旋度。谱螺旋度分解可用于周期性区域，对分析均匀现象是富有成效的。本文的目的是发展的方法，用于分析在非均匀系统中的磁场拓扑结构的演变。方法.将多分辨率小波分解方法应用于磁场分析。它演示了如何分解可以进一步应用到各种数量与磁螺旋度，包括磁力线螺旋度。我们使用螺旋度的几何定义，它允许这些数量计算任意边界条件的字段。结果证明了螺旋度的多分辨分解具有局部可加性的重要性质。我们证明了一个一般的线性能量拓扑守恒律，显着推广了两点相关分解用于均匀湍流和周期性领域的分析。小波表示的局部化特性被证明可以表征非均匀分布，而傅里叶表示则不能。使用电阻性编织场松弛的解析表示，我们证明了在不同的长度尺度上的能量变化和在相同的空间尺度上的螺旋度的变化之间的明确的相关性。它的应用程序中的表面通量传输模式的螺旋度流显示如何从活动区域场的演变和极场的发展的各种贡献的全球螺旋度输入自然分离的这种表示。结论.多分辨率小波分解可以用来分析螺旋度在磁场中的演化，其方式是一致的加性。这种方法的优势，在更成熟的光谱方法，它清楚地表征螺旋度流的非均匀性，光谱方法不能。此外，它在非周期模型的适用性显着增加了潜在的应用范围。
Context. Magnetic helicity is approximately conserved in resistive magnetohydrodynamic models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both dynamo development in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement. Aims. There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods. The method of multi-resolution wavelet decomposition is applied to the magnetic field. It is demonstrated how this decomposition can further be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity, which allows these quantities to be calculated for fields with arbitrary boundary conditions. Results. It is shown that the multi-resolution decomposition of helicity has the crucial property of local additivity. We demonstrate a general linear energy-topology conservation law, which significantly generalises the two-point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions, which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation, we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation. Conclusions. The multi-resolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further, its applicability in aperiodic models significantly increases the range of potential applications.