arXiv 1302.47282013-02-19astro-ph.SR

短波长磁浮力不稳定性

Short wavelength magnetic buoyancy instability

K. A. Mizerski, C. R. Davies, D. W. Hughes

备注：: Accepted for publication by ApJ Suppl
DOI：: 10.1088/0067-0049/205/2/16

摘要：

磁浮力不稳定性在天体物理磁场演化中起着重要作用。在这里，我们重新讨论的问题所介绍的\citet{Gilman_1970}的短波长线性稳定性的平面层的可压缩等温流体渗透的水平磁场的强度随高度而下降。忽略动量和磁场的耗散。利用瑞利-薛定谔微扰分析，详细解释了微扰的横向水平波数（用$k$表示）大（即\短的水平波长），并表明随着$k$的增加，增长最快的扰动变得局限于垂直方向。生长速率由垂直坐标$z$的函数确定，因为在大的$k$极限中，本征模强烈地定位在垂直方向上。我们详细考虑的情况下，二维扰动变化的方向垂直于磁场，其中，足够强的磁场梯度，是最不稳定的。通过与一系列初值问题的比较，我们的分析结果得到了支持。最后，我们扩展到三维扰动的分析。

英文摘要：

Magnetic buoyancy instability plays an important role in the evolution of astrophysical magnetic fields. Here we revisit the problem introduced by \citet{Gilman_1970} of the short wavelength linear stability of a plane layer of compressible isothermal fluid permeated by a horizontal magnetic field of strength decreasing with height. Dissipation of momentum and magnetic field is neglected. By the use of a Rayleigh-Schrödinger perturbation analysis, we explain in detail the limit in which the transverse horizontal wavenumber of the perturbation, denoted by $k$, is large (i.e.\ short horizontal wavelength) and show that the fastest growing perturbations become localized in the vertical direction as $k$ is increased. The growth rates are determined by a function of the vertical coordinate $z$ since, in the large $k$ limit, the eigenmodes are strongly localized in the vertical direction. We consider in detail the case of two-dimensional perturbations varying in the directions perpendicular to the magnetic field, which, for sufficiently strong field gradients, are the most unstable. The results of our analysis are backed up by comparison with a series of initial value problems. Finally we extend the analysis to three-dimensional perturbations.

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