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非线性共振Alfven波产生的平均剪切流

Mean shear flows generated by nonlinear resonant Alfven waves

C. T. M. Clack, I. Ballai

备注：
11 pages
发表信息：
Phys. Plasmas 16, 072115 (2009)
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摘要：

在共振吸收的情况下，非线性有两种不同的表现。第一个是谐振点周围扰动幅度的减小（波能吸收）。第二种是在共振点周围的耗散层外产生平均剪切流。Ruderman等人[Phys. Plasmas 4，75（1997）]研究了各向同性等离子体中慢共振时的这两种效应。Clack等人[Astron. Astrophys. 494}，317（2009）]研究了Alfven共振处的非线性，然而，它们不包括平均剪切流的产生。在本文中，我们研究平均剪切流，解析，并研究其性质。我们发现，产生的流动是平行的磁表面，并有一个特征速度成正比的$ε^{1/2}$，其中$ε$是无量纲振幅的扰动远离共振。这在性质上类似于在慢共振时产生的流动。导出了穿过耗散层的平均剪切流的平行分量和垂直分量的导数的跳跃。我们估计产生的平均剪切流在太阳上色球层和日冕的顺序为$10{\rm kms}^{-1}$，然而，这个值强烈地依赖于边界条件的选择。它提出，所产生的平均剪切流可以产生一个Kelvin-Helmholtz不稳定性的耗散层，可以创建湍流运动。这种不稳定性将是一个额外的影响，因为开尔文-亥姆霍兹不稳定性可能已经存在，由于共振阿尔芬波的速度场。这种流动也可以叠加到太阳高层大气中现有的大尺度运动上。

英文摘要：

In the context of resonant absorption, nonlinearity has two different manifestations. The first is the reduction in amplitude of perturbations around the resonant point (wave energy absorption). The second is the generation of mean shear flows outside the dissipative layer surrounding the resonant point. Ruderman et al. [Phys. Plasmas 4, 75 (1997)] studied both these effects at the slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys. 494}, 317 (2009)] investigated nonlinearity at the Alfven resonance, however, they did not include the generation of mean shear flow. In this present paper, we investigate the mean shear flow, analytically, and study its properties. We find that the flow generated is parallel to the magnetic surfaces and has a characteristic velocity proportional to $ε^{1/2}$, where $ε$ is the dimensionless amplitude of perturbations far away from the resonance. This is, qualitatively, similar to the flow generated at the slow resonance. The jumps in the derivatives of the parallel and perpendicular components of mean shear flow across the dissipative layer are derived. We estimate the generated mean shear flow to be of the order of $10{\rm kms}^{-1}$ in both the solar upper chromosphere and solar corona, however, this value strongly depends on the choice of boundary conditions. It is proposed that the generated mean shear flow can produce a Kelvin--Helmholtz instability at the dissipative layer which can create turbulent motions. This instability would be an additional effect, as a Kelvin--Helmholtz instability may already exist due to the velocity field of the resonant Alfven waves. This flow can also be superimposed onto existing large scale motions in the solar upper atmosphere.

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