Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation
Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation
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瑞利极限和准开普勒旋转泰勒-库埃特流的螺旋磁旋转不稳定性
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发表时间：
2008
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通讯作者：
M. Schultz
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作者：
G. Ruediger;M. Schultz
在无电流磁场的轴向分量和方位分量同时存在的情况下，考虑了差动旋转的磁旋转不稳定性。对于具有均匀比角动量的转动，在局部短波近似下求解了轴对称微扰的MHD方程。对于本征频率接近粘性频率的BZ·Bϕ≠0，所有解都是超稳定的。对于更平坦的旋转律，局部近似的结果与旋转圆柱间Taylor-Couette流动的MHD不稳定性的整体计算结果不一致。-在B、ϕ和BZ相同阶的情况下，对于准开普勒转动等平转定律，行波模解也是首选的。对于磁普朗特数Pm0，它们随旋转的雷诺数而不是与磁雷诺数(就像标准磁共振一样)成比例，因此它们可以很容易地在MHD实验室实验中实现。-对于非轴对称模式，我们发现B、ϕ/BZ之比只对极值有显着影响。对于B、ϕ≫、BZ和PM不太小的情况，非轴对称模式在行波轴对称模式中占主导地位。然而，对于具有BZ≫Bϕ的标准磁共振成像，非轴对称模式的临界雷诺数比轴对称模式的值高出许多个数量级，因此它们从来都不是首选的。(2018Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current-free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short-wave approximation. All the solutions are overstable for Bz · Bϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor-Couette flows between rotating cylinders. – With Bϕ and Bz of the same order the traveling-mode solutions are also prefered for flat rotation laws such as the quasi-Kepler rotation. For magnetic Prandtl number Pm 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio Bϕ/Bz only for the extrema. For Bϕ ≫ Bz and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with Bz ≫ Bϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)