Planar channel flow in Braginskii magnetohydrodynamics
Planar channel flow in Braginskii magnetohydrodynamics
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DOI：
10.1017/s0022112010004507
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发表时间：
2011-01
影响因子：
3.7
通讯作者：
P. Dellar
中科院分区：
文献类型：
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作者：
P. Dellar
Braginskii磁流体动力学（MHD）是一种描述强磁化等离子体中大尺度运动的单流体模型。这些等离子体中的离子拉莫尔半径比碰撞之间的平均自由程短得多，因此穿过磁场线的动量传输被强烈抑制。应变率和粘性应力之间的关系变得高度各向异性，粘性应力主要平行于磁场排列。我们对布拉金斯基磁流体动力学中由沿直通道的均匀压力梯度驱动的施加均匀磁场中的稳定平面流进行了分析研究，该结构称为哈特曼流。沿着直通道。仅通过平行的粘性应力不能满足整体动量平衡，因此我们还包括垂直于磁力线的粘性应力。在我们的分析中，垂直粘度与平行粘度之比是关键的小参数。当另一个参数，哈特曼数，是大的流动是均匀的，通过大部分的通道，与边界层的任何一个墙上的修改的哈特曼层在标准各向同性MHD。然而，哈特曼层的解决方案预测一个无限大的电流和无限大的剪切在墙上，符合当地的一系列解决方案的基本微分方程，是有效的所有哈特曼数。这些奇异性是由内边界层解决的，其宽度尺度为粘度比的四分之三幂，而最大速度尺度为粘度比的四分之一幂的倒数。内壁层配合在哈特曼层（如果存在）和壁之间。由于粘度比趋于零，因此溶液不会接近极限。解的基本特征，如最大流速和最大流速，由粘性比的大小决定，粘性比是正则化的小参数。
Braginskii magnetohydrodynamics (MHD) is a single-fluid description of large-scale motions in strongly magnetised plasmas. The ion Larmor radius in these plasmas is much shorter than the mean free path between collisions, so momentum transport across magnetic field lines is strongly suppressed. The relation between the strain rate and the viscous stress becomes highly anisotropic, with the viscous stress being predominantly aligned parallel to the magnetic field. We present an analytical study of the steady planar flow across an imposed uniform magnetic field driven by a uniform pressure gradient along a straight channel, the configuration known as Hartmann flow, in Braginskii MHD. The global momentum balance cannot be satisfied by just the parallel viscous stress, so we include the viscous stress perpendicular to magnetic field lines as well. The ratio of perpendicular to parallel viscosities is the key small parameter in our analysis. When another parameter, the Hartmann number, is large the flow is uniform across most of the channel, with boundary layers on either wall that are modifications of the Hartmann layers in standard isotropic MHD. However, the Hartmann layer solution predicts an infinite current and infinite shear at the wall, consistent with a local series solution of the underlying differential equation that is valid for all Hartmann numbers. These singularities are resolved by inner boundary layers whose width scales as the three-quarters power of the viscosity ratio, while the maximum velocity scales as the inverse one-quarter power of the viscosity ratio. The inner wall layers fit between the Hartmann layers, if present, and the walls. The solution thus does not approach a limit as the viscosity ratio tends to zero. Essential features of the solution, such as the maximum current and maximum velocity, are determined by the size of the viscosity ratio, which is the regularising small parameter.