横向磁场作用下流动的有效二维模型的数值模拟
Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field
摘要：
本文模拟了Pothérat等人（\emph{J. Fluid Mech}，2000）建立的二维模型，该模型用于考虑Hartmann层中的中等惯性效应，在强横向均匀和稳定的磁场作用下，两个平面之间的MHD流动。我们首先分析了如何在运动方程中的附加项占惯性，软化在水平面上的速度梯度，然后我们实现了一个代码上的模型进行数值模拟与现有的实验结果进行比较。这种比较表明，只要哈特曼层保持层流，新模型就能给出非常精确的结果。两个实验的速度分布和全球角动量测量密切恢复，和本地和全球埃克曼回流显着改变方面的流量以及全球耗散。
英文摘要：
This paper presents simulations of the 2d model developed by Pothérat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms in the equations of motion accounting for inertia, soften velocity gradients in the horizontal plane, and then we implement the model on a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are closely recovered, and local and global Ekman recirculations are shown to alter significantly the aspect of the flow as well as the global dissipation.
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