Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow.
Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow.
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泰勒-库埃特流中的绝对与对流螺旋磁旋转不稳定性。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Gerbeth
中科院分区：
文献类型：
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作者：
J. Priede;G. Gerbeth
用零磁Prandtl数(Prm}=0)定义的无感近似，数值分析了Taylor-Couette流在螺旋磁场中的磁旋不稳定性(HMRI).用切比雪夫配置法计算了小振幅扰动的本征值谱。首先，我们对傅立叶模形式的摄动进行了详细的常规线性稳定性分析，该摄动对应于对流不稳定，而对流不稳定通常不是自持续的。研究发现，螺旋磁场将不稳定性扩展到相对较窄的范围，超出了瑞利线所定义的纯流体动力学极限。HMRI不仅有一个较低的临界阈值出现，而且有一个较高的阈值再次消失。后者将HMRI与磁性修正的泰勒涡流区分开来。其次，我们还发现了一个绝对不稳定的门槛。在瑞利线之前的流体动力不稳定区域，绝对不稳定的阈值仅略高于对流不稳定阈值，但前者的临界波长明显短于对流不稳定阈值。在瑞利线以外，绝对不稳定的下限阈值显着高于对流不稳定阈值，而上不稳定阈值显着低于对流不稳定阈值。结果表明，绝对HMRI在瑞利线以外的延展比对流不稳定性的延展要短得多。绝对的HMRI应该是自维持的，因此，在一个轴向伸展足够大的系统中，在没有任何外部激励的情况下，实验上是可以观察到的。
We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number (Pr_{m}=0) . The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.