arXiv 2303.145472023-03-25physics.flu-dyn

间隙尺寸对圆柱Couette流中磁旋转不稳定性激发的影响

The gap-size influence on the excitation of magnetorotational instability in cylindrical Couette flows

G. Rüdiger, M. Schultz

备注：: 12 pages, 6 figures

摘要：

本文研究了不同间隙宽度的轴向无限泰勒-库埃特流的磁旋转不稳定性的激发条件。圆柱体被认为是由完美的导电或绝缘材料和导电流体有限，但小的磁性普朗特数旋转的准开普勒速度分布。该解决方案是优化相对于波数和雷诺数的内圆筒的旋转。对于轴对称模式，我们发现所施加的轴向磁场的临界Lundquist数越低，圆柱之间的间隙越宽。对于诱导细胞结构获得了类似的结果：间隙越宽，细胞越球形。对于固定尺寸的外筒，内筒的边际转速在间隙宽度不太宽和不太窄的情况下总是具有最小值。对于理想导电壁，最小值位于$r_{\rm in}\simeq 0.4$，而对于绝缘壁，最小值位于$r_{\rm in}\simeq 0.5$，其中$r_{\rm in}$是内圆柱的归一化半径。激发不稳定性的最低磁场幅值是理想导电圆柱体之间的泰勒-库埃特流所需的，其间隙对应于$r_{\rm in}\simeq 0.2$。对于甚至更宽的间隙和非常薄的间隙，所需的磁场和旋转频率被示出为变得相当巨大。还考虑了含$|m|=1$的非轴对称模式。与轴对称模式相比，它们的激励通常需要更强的磁场和更高的磁雷诺数，这对于具有$r_{\rm in} \lesssim 0.3$的宽间隙容器是真实的。

英文摘要：

The excitation conditions of the magnetorotational instability are studied for axially unbounded Taylor-Couette flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wave number and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes we find the critical Lundquist number of the applied axial magnetic field the lower the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap the more spherical the cells are. The marginal rotation rate of the inner cylinder -- for fixed size of the outer cylinder -- always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{\rm in}\simeq 0.4$ while it is at $r_{\rm in}\simeq 0.5$ for insulating walls where $r_{\rm in}$ is the normalized radius of the inner cylinder. The lowest magnetic field amplitudes to excite the instability are required for Taylor-Couette flows between perfect-conducting cylinders with gaps corresponding to $r_{\rm in}\simeq 0.2$. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the nonaxisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison to those for the axisymmetric modes which is true for wide-gap containers with $r_{\rm in} \lesssim 0.3$.

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