Hartmann Flow with Braginsky Viscosity: A Test Problem for Plasma in the Intracluster Medium
Hartmann Flow with Braginsky Viscosity: A Test Problem for Plasma in the Intracluster Medium
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具有布拉金斯基粘度的哈特曼流：簇内介质中等离子体的测试问题
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发表时间：
2008
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通讯作者：
M. Lyutikov
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作者：
M. Lyutikov
在回转等离子体极限下，考虑粘性流体和阻性流体在横向磁场叠加的平板之间的定常Hartmann层流动，场中粘性流体的粘性被强烈抑制。对于零交叉场粘性，问题不是很好地解决，因为粘性随后在边界和层的中间消失，那里没有纵向场。附加的任意小的各向同性粘度使人们能够找到与该粘度底线无关的磁场和速度分布，并且不同于具有各向同性粘度的流动。在薄边界层中，速度急剧上升，边界层的厚度既取决于流动的哈特曼数，也取决于流动的Lundquist数。这项工作的含义是，在模拟ICM动力学时，必须使用考虑各向异性粘性的数值格式。尽管磁场在ICM中处于动态次要地位，但它们确实决定了ICM的耗散特性、嵌入结构的稳定性以及向湍流的过渡。
We consider a Hartmann layer, stationary flow of a viscose and resistive fluid between two plates with superimposed transverse magnetic field, in the limit of gyrotropic plasma, when viscosity across the field is strongly suppressed. For zero cross-field viscosity, the problem is not well posed, since viscosity then vanishes on the boundaries and in the middle of the layer, where there is no longitudinal field. An additional arbitrarily small isotropic viscosity allows one to find magnetic field and velocity profiles that are independent of this viscosity floor and different from flows with isotropic viscosity. Velocity sharply rises in a thin boundary layer, and the thinness of this boundary layer depends both on the Hartmann number and on the Lundquist number of the flow. The implication of the work is that, in simulating ICM dynamics, it is imperative to use numerical schemes that take into account anisotropic viscosity. Although magnetic fields are dynamically subdominant in the ICM, they do determine its dissipative properties, the stability of embedded structures, and the transition to turbulence.