Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow
Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow
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磁化 TaylorâCouette 流中螺旋磁旋转不稳定性的准二维非线性演化
DOI：
10.1088/1367-2630/aa9d65
复制
发表时间：
2018
影响因子：
3.3
通讯作者：
M. Avila
中科院分区：
文献类型：
--
作者：
G. Mamatsashvili;F. Stefani;A. Guseva;M. Avila
磁旋转不稳定性（MRI）是天体物理学的基本过程之一，驱动各种宇宙物体的角动量传输和质量吸积。尽管在过去的几十年里进行了大量的理论/数值和实验工作，但其饱和机制和决定角动量输运率的振幅仍然没有得到很好的理解，特别是在高电阻率或实验室中原行星盘、行星液体核心和液态金属内部（死区）典型的小磁普朗特数的限制下。在本文中，我们使用直接数值模拟研究了与液态金属相关的极低磁普朗特数（相应地低磁雷诺数）磁化泰勒-库埃特流中螺旋磁旋转不稳定性（HMRI）（与标准 MRI 的相对）的非线性发展和饱和特性。为简单起见，方位角场与轴向场的比率保持固定。从HMRI的线性理论可知，Elsasser数或相互作用参数决定了其增长率并在动力学中起着特殊的作用。我们证明这个参数在非线性问题中也很重要。通过增加其值，系统会突然从弱非线性（系统略高于线性稳定性阈值）过渡到强非线性或湍流状态。我们计算了这两种状态对应的方位角和轴向能谱，并表明它们有质的不同。值得注意的是，非线性状态在所有情况下都保持近轴对称，这表明这种 HMRI 驱动的湍流本质上是准二维的。尽管非轴对称模式的贡献随着 Elsasser 数的增加而适度增加，但它们的总能量仍然比轴对称模式小得多。
Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor–Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.
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DOI：
--
发表时间：
2013
期刊：
影响因子：
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作者：
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通讯作者：
C. Charbonnel
影响因子：
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作者：
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DOI：
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发表时间：
2008
期刊：
影响因子：
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DOI：
--
发表时间：
2008
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
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作者：
J. Priede;G. Gerbeth
通讯作者：
G. Gerbeth
影响因子：
3.3
作者：
Guseva, A.;Willis, A. P.;Avila, M.
通讯作者：
Avila, M.