NONLOCAL STABILITY ANALYSIS OF THE MHD KELVIN-HELMHOLTZ INSTABILITY IN A COMPRESSIBLE PLASMA
NONLOCAL STABILITY ANALYSIS OF THE MHD KELVIN-HELMHOLTZ INSTABILITY IN A COMPRESSIBLE PLASMA
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DOI：
10.1029/ja087ia09p07431
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发表时间：
1982-01-01
影响因子：
2.8
通讯作者：
PRITCHETT, PL
中科院分区：
文献类型：
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作者：
MIURA, A;PRITCHETT, PL
对可压缩等离子体中有限厚度剪切磁流体动力学流的Kelvin-Helmholtz不稳定性进行了一般稳定性分析。该分析允许磁场B 0、速度流v0和波矢量在垂直于速度梯度的平面内的任意取向，并且对声音或阿尔文马赫数没有限制。稳定性问题被简化为一个二阶微分方程的解，其中包括一个引力项来表示开尔文-亥姆霍兹模式和交换模式之间的耦合。在不可压缩的极限，它表明，开尔文-亥姆霍兹模式是完全稳定的任何速度分布，只要条件 其中V0是剪切层上的总速度跃变。数值结果得到的双曲正切速度分布的横向（B 0 v0）和平行（B 0 v0）流配置。只有k Δ < 2的模态是不稳定的，其中Δ是剪切层的标度长度。增长最快的模式出现在Δ ε 0.5 - 1.0。可压缩性和磁场分量平行的流动被发现是稳定的效果。在横向情况下，只有快磁声模失稳，但如果k·B 0 ≥ 0，则失稳也包含Alfvén模和慢模分量。Alfvén分量在剪切层内部产生场向电流。在平行的情况下，阿尔文和慢磁声分量都存在，阿尔文模式被限制在剪切层内。分析结果被用来讨论磁层顶边界和太阳风中剪切等离子体流的稳定性。在磁层顶边界，增长最快的开尔文-亥姆霍兹模式的频率为0（V0/2Δ），与地磁脉动的频率范围（Pc 3 - 5）重叠。这表明，MHD开尔文-亥姆霍兹不稳定性可以作为一个发电机过程驱动小尺度场向电流在磁层中的剪切等离子体流的存在。
A general stability analysis is performed for the Kelvin‐Helmholtz instability in sheared magnetohydrodynamic flow of finite thickness in a compressible plasma. The analysis allows for arbitrary orientation of the magnetic fieldB0, velocity flowv0, and wave vectorkin the plane perpendicular to the velocity gradient, and no restrictions are imposed on the sound or Alfvén Mach numbers. The stability problem is reduced to the solution of a single second‐order differential equation, which includes a gravitational term to represent coupling between the Kelvin‐Helmholtz mode and the interchange mode. In the incompressible limit it is shown that the Kelvin‐Helmholtz mode is completely stabilized for any velocity profile as long as the condition is satisfied, whereV0is the total velocity jump across the shear layer. Numerical results are obtained for a hyperbolic tangent velocity profile for the transverse (B0⊥v0) and parallel (B0∥v0) flow configurations. Only modes withkΔ < 2 are unstable, where Δ is the scale length of the shear layer. The fastest growing modes occur forkΔ ∼ 0.5‐1.0. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects. For the transverse case, only the fast magnetosonic mode is destabilized, but ifk · B0≠ 0, the instability contains Alfvén‐mode and slow‐mode components as well. The Alfvén component gives rise to a field‐aligned current inside the shear layer. In the parallel case, both Alfvén and slow magnetosonic components are present, with the Alfvén mode confined inside the shear layer. The results of the analysis are used to discuss the stability of sheared plasma flow at the magnetopause boundary and in the solar wind. At the magnetopause boundary, the fastest growing Kelvin‐Helmholtz mode has a frequency of 0 (V0/2Δ), which overlaps with the frequency range of geomagnetic pulsations (Pc 3‐5). It is suggested that the MHD Kelvin‐Helmholtz instability could serve as a dynamo process driving small‐scale field‐aligned currents in the presence of the sheared plasma flow in the magnetosphere.