An analytical study of the MHD clamshell instability on a sphere
An analytical study of the MHD clamshell instability on a sphere
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DOI：
10.1017/jfm.2022.973
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发表时间：
2022-09
影响因子：
3.7
通讯作者：
Chen Wang;A. Gilbert;J. Mason
中科院分区：
文献类型：
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作者：
Chen Wang;A. Gilbert;J. Mason
本文用解析方法研究了球面上二维磁流体系统的不稳定性。基本流动由纬向差动旋转和环向磁场组成。导出了一般流场和场分布的复平面内波速的可能范围的半圆规则。然后，本文提出了一个‘翻盖不稳定性’的分析研究，它的特点是两个半球上的场线向相反的方向倾斜(Cally，Sol.物理，第199卷，2001年，第231-249页)。利用匹配渐近展开的方法，得到了纬向流弱切变极限下不稳定问题的渐近解。结果表明，当纬向流为固体自转时，存在一个使磁力线倾斜的中性模式，称为倾斜模式。纬向流的弱切变激发倾斜模的临界层，使倾斜模的倾斜方向发生反转，形成翻壳型，导致不稳定。渐近解提供了对一系列流动和场分布的不稳定性特性的洞察。一个显著的特征是，磁场只通过其在临界层的局部行为来影响不稳定性。
Abstract This paper studies the instability of two-dimensional magnetohydrodynamic 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, Sol. Phys., vol. 199, 2001, 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.