Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications
Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications
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任意磁拓扑的 Braginskii 磁流体动力学：日冕应用
DOI：
10.1017/jfm.2017.463
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发表时间：
2017
影响因子：
3.7
通讯作者：
MacTaggart D
中科院分区：
文献类型：
--
作者：
MacTaggart D
我们调查单流体磁流体动力学（MHD）与各向异性粘度，通常被称为Braginskii MHD，特别着眼于太阳日冕的应用。首先，我们研究了完整的Braginskii粘性张量在单流体极限。我们特别注意如何Braginskii张量表现为磁场强度为零。日冕包含一个具有复杂和不断发展的拓扑结构的磁场，因此当场强为零时，粘度必须恢复到其各向同性形式，例如在零点。我们强调，标准形式中的Braginskii张量是书面的是不适合列入在模拟中的奇性，在个别条款可以开发。相反，一个改变的形式，其中的平行和垂直张量相结合，提供了所需的渐近行为在弱场极限。我们将张量的这种组合形式实现到Lare3D代码中，该代码广泛用于冠状模拟。由于我们的主要焦点是太阳日冕的粘性加热，我们放弃了Braginskii张量的漂移项。在应力零点模拟中，我们发现，小尺度结构，发展非常接近零，导致各向异性粘性加热在零本身（即，加热由于各向异性项的粘度张量）。我们提出的零点模拟比许多其他包含零点的模拟具有更高的分辨率，因此这种过度加热在日冕模拟中是一个实际问题。为了弥补这种不必要的加热在零点，我们开发了一个模型的粘度张量，捕捉最重要的物理粘度在日冕：平行粘度强场和各向同性粘度在零点。我们推导出一个连续介质模型的粘度动量输运，由这个粘度模型描述，有磁场作为其首选方向。当场强为零时，动量传输没有优选方向，粘度恢复到标准各向同性形式。找到了满足这些条件的（单流体）等离子体的最一般的粘性应力张量，表明不含漂移项的Braginskii模型是一般模型的特殊化。用这种简化的粘度模型进行应力零点模拟，揭示了与完整Braginskii模型非常相似的加热曲线。然而，新的模型，不产生各向异性加热的零点，如所需的。由于绝大多数日冕模拟仅使用各向同性粘性，因此我们使用各向同性粘性执行应力零点模拟，并将加热曲线与各向异性模型的加热曲线进行比较。结果表明，完全各向同性的粘度可以高估一个数量级的粘性加热。
We investigate single-fluid magnetohydrodynamics (MHD) with anisotropic viscosity, often referred to as Braginskii MHD, with a particular eye to solar coronal applications. First, we examine the full Braginskii viscous tensor in the single-fluid limit. We pay particular attention to how the Braginskii tensor behaves as the magnetic field strength vanishes. The solar corona contains a magnetic field with a complex and evolving topology, so the viscosity must revert to its isotropic form when the field strength is zero, e.g. at null points. We highlight that the standard form in which the Braginskii tensor is written is not suitable for inclusion in simulations as singularities in the individual terms can develop. Instead, an altered form, where the parallel and perpendicular tensors are combined, provides the required asymptotic behaviour in the weak-field limit. We implement this combined form of the tensor into the Lare3D code, which is widely used for coronal simulations. Since our main focus is the viscous heating of the solar corona, we drop the drift terms of the Braginskii tensor. In a stressed null point simulation, we discover that small-scale structures, which develop very close to the null, lead to anisotropic viscous heating at the null itself (that is, heating due to the anisotropic terms in the viscosity tensor). The null point simulation we present has a much higher resolution than many other simulations containing null points, so this excess heating is a practical concern in coronal simulations. To remedy this unwanted heating at the null point, we develop a model for the viscosity tensor that captures the most important physics of viscosity in the corona: parallel viscosity for strong fields and isotropic viscosity at null points. We derive a continuum model of viscosity where momentum transport, described by this viscosity model, has the magnetic field as its preferred orientation. When the field strength is zero, there is no preferred direction for momentum transport and viscosity reverts to the standard isotropic form. The most general viscous stress tensor of a (single-fluid) plasma satisfying these conditions is found. It is shown that the Braginskii model, without the drift terms, is a specialization of the general model. Performing the stressed null point simulation with this simplified model of viscosity reveals very similar heating profiles to those of the full Braginskii model. The new model, however, does not produce anisotropic heating at the null point, as required. Since the vast majority of coronal simulations use only isotropic viscosity, we perform the stressed null point simulation with isotropic viscosity and compare the heating profiles to those of the anisotropic models. It is shown that the fully isotropic viscosity can overestimate the viscous heating by an order of magnitude.
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