Inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field.
Inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field.
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螺旋磁场泰勒-库埃特流中的无感应磁旋转不稳定性。
DOI：
10.1088/1742-6596/64/1/012011
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
G. Gerbeth
中科院分区：
文献类型：
--
作者：
J. Priede;I. Grants;G. Gerbeth
在由零磁Prandtl数(Pm=0)定义的无感近似下，我们考虑了流体动力学稳定的Taylor-Couette流的磁旋转不稳定性(MRI)。这导致问题得到相当大的简化，最终只包含流体动力学变量。首先，我们指出，磁场增加了更多的耗散，而不改变基流，基流是不断增长的微扰的唯一能量来源。因此，从能量的角度来看，似乎不清楚这种流体动力学稳定的流动如何在螺旋磁场的存在下变得不稳定，就像最近由Hollerbach和Rüdiger[Phys]发现的那样。莱特牧师。95,124501(2005年)]。我们用切比雪夫配置法计算了线性化问题的特征值谱，从而重新讨论了这个问题。通过这种方式，我们证实了在无感应近似下，螺旋磁场确实可以使流动不稳定。其次，我们对线性化后的方程进行了时间积分，研究了小幅度扰动的暂态行为，从而证明了能量守恒定律的正确性。然而，这两个事实之间并不存在真正的矛盾。线性稳定性理论预测任意小幅度扰动的渐近发展，而能量稳定性理论给出任何特定扰动的瞬时增长率，但它不能解释这种扰动的演化。因此，尽管接通磁场会立即增加主要流体动力学扰动的能量衰减率，但同时，在磁场存在的情况下，该扰动不再是本征模。因此，这种扰动随时间变化，因此能够从增长所需的基流中提取能量。
We consider the magnetorotational instability (MRI) of a hydrodynamically stable Taylor-Couette flow with a helical external magnetic field in the inductionless approximation defined by a zero magnetic Prandtl number (Pm=0) . This leads to a considerable simplification of the problem eventually containing only hydrodynamic variables. First, we point out that magnetic field adds more dissipation while it does not change the base flow which is the only source of energy for growing perturbations. Thus, it seems unclear from the energetic point of view how such a hydrodynamically stable flow can turn unstable in the presence of a helical magnetic field as it has been found recently by Hollerbach and Rüdiger [Phys. Rev. Lett. 95, 124501 (2005)]. We revisit this problem by using a Chebyshev collocation method to calculate the eigenvalue spectrum of the linearized problem. In this way, we confirm that a helical magnetic field can indeed destabilize the flow in the inductionless approximation. Second, we integrate the linearized equations in time to study the transient behavior of small amplitude perturbations, thus showing that the energy arguments are correct as well. However, there is no real contradiction between both facts. The linear stability theory predicts the asymptotic development of an arbitrary small-amplitude perturbation, while the energy stability theory yields the instant growth rate of any particular perturbation, but it does not account for the evolution of this perturbation. Thus, although switching on the magnetic field instantly increases the energy decay rate of the dominating hydrodynamic perturbation, in the same time this perturbation ceases to be an eigenmode in the presence of the magnetic field. Consequently, this perturbation is transformed with time and so becomes able to extract energy from the base flow necessary for the growth.