论文标题
对球体上MHD蛤shell不稳定性的分析研究
An analytical study of the MHD clamshell instability on a sphere
论文作者
论文摘要
本文使用分析方法研究了球体上二维磁流失动力（MHD）系统的不稳定性。下面的流由区域差分旋转组成，并且存在环形磁场。得出了在复杂平面中为一般流量和场剖面中波浪速度规定波速的可能结构域的半圆规则。然后，该论文对“翻盖式不稳定性”的分析研究提出了一项分析研究，该研究的特征是两个半球朝相反方向倾斜的场线（Cally 2001，Sol。Phys。Vol。199，第231---249页）。通过匹配的渐近膨胀方法，针对区域流量弱剪切的极限得出了针对不稳定性问题的渐近解决方案。结果表明，当区域流量是实体旋转时，存在一种中性模式，将磁场线倾斜，称为“倾斜模式”。纬向流的弱剪切刺激了倾斜模式的临界层，这逆转了倾斜方向以形成蛤壳模式并诱导不稳定性。渐近解决方案为一系列流量和场曲线的不稳定性的特性提供了见解。一个显着的特征是，磁场仅通过临界层中的局部行为影响不稳定性。
This paper studies the instability of two-dimensional magnetohydrodynamic (MHD) systems on a sphere using analytical methods. The underlying flow consists of a zonal differential rotation and a toroidal magnetic field is present. Semicircle rules that prescribe the possible domain of the wave velocity in the complex plane for general flow and field profiles are derived. The paper then sets out an analytical study of the `clamshell instability', which features field lines on the two hemispheres tilting in opposite directions (Cally 2001, Sol. Phys. vol. 199, pp. 231--249). An asymptotic solution for the instability problem is derived for the limit of weak shear of the zonal flow, via the method of matched asymptotic expansions. It is shown that when the zonal flow is solid body rotation, there exists a neutral mode that tilts the magnetic field lines, referred to as the `tilting mode'. A weak shear of the zonal flow excites the critical layer of the tilting mode, which reverses the tilting direction to form the clamshell pattern and induces the instability. The asymptotic solution provides insights into properties of the instability for a range of flow and field profiles. A remarkable feature is that the magnetic field affects the instability only through its local behaviour in the critical layer.
