On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
复制标题
关于瑞利稳定旋转平面库埃特流中的自持过程和吸积盘中亚临界过渡到湍流
DOI：
10.1051/0004-6361:20066544
复制
发表时间：
2006
影响因子：
6.5
通讯作者：
C. Cossu
中科院分区：
文献类型：
--
作者：
F. Rincon;Gordon I. Ogilvie;C. Cossu
上下文。开普勒吸积盘的亚临界向湍流转变仍然是一个有争议的问题，需要一些理论上的进展才能确定这一情景是否为非磁化吸积盘中角动量输运的起源提供了合理的解释。目标。受最近在线性稳定的非旋转剪切流中发现的精确的非线性定常自持解的启发，我们试图计算Rayleigh稳定的旋转平面Couette流中的类似解，并确定这种流动中的过渡机制。方法：研究方法。数值模拟(时间步长方法)已被用于最近对该问题的研究。这里，我们将非线性连续方法和渐近理论结合起来，研究Rayleigh稳定区平面Couette流的非线性动力学。结果。我们利用Waleffe和Nagata提出的延拓技术得到了Rayleigh稳定气旋区的精确的非线性解，但表明不可能用类似的方法计算Rayleigh稳定的反气旋区的解，包括开普勒流。我们还给出了这些问题在大雷诺数下的渐近描述，从而揭示了非旋转反气旋和瑞利稳定反气旋之间的区别，并导出了一些类似于非旋转自持过程的机制存在于瑞利线上的(常角动量)流动中的必要条件。结论。我们的结果表明，在壁面Rayleigh稳定的反气旋切变流中，不能通过直接颠倒旋风和非旋转壁面切变流中的亚临界转变现象来识别亚临界转变机制。然而，渐近的发展留下了在瑞利线上的无界或周期流动中存在非线性自维持解的可能性。这些可以作为在瑞利稳定流中寻找解的起点，但开普勒吸积盘的非线性稳定性仍有待确定。
Context. Subcritical transition to turbulence in Keplerian accretion disks is still a controversial issue and some theoretical progress is required in order to determine whether or not this scenario provides a plausible explanation for the origin of angular momentum transport in non-magnetized accretion disks. Aims. Motivated by the recent discoveries of exact nonlinear steady self-sustaining solutions in linearly stable non-rotating shear flows, we attempt to compute similar solutions in Rayleigh-stable rotating plane Couette flows and to identify transition mechanisms in such flows. Methods. Numerical simulations (time-stepping approaches) have been employed in most recent studies of the problem. Here, we instead combine nonlinear continuation methods and asymptotic theory to study the nonlinear dynamics of plane Couette flows in Rayleigh-stable regimes. Results. We obtain exact nonlinear solutions for Rayleigh-stable cyclonic regimes using continuation techniques proposed by Waleffe and Nagata but show that it is not possible to compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian flow, using similar techniques. We also present asymptotic descriptions of these various problems at large Reynolds numbers that provide some insight into the differences between the non-rotating and Rayleigh-stable anticyclonic regimes and derive some necessary conditions for mechanisms analogous to the non-rotating self-sustaining process to be present in (constant angular momentum) flows on the Rayleigh line. Conclusions. Our results demonstrate that subcritical transition mechanisms cannot be identified in wall-bounded Rayleigh-stable anticyclonic shear flows by transposing directly the phenomenology of subcritical transition in cyclonic and non-rotating wall-bounded shear flows. Asymptotic developments, however, leave open the possibility that nonlinear self-sustaining solutions may exist in unbounded or periodic flows on the Rayleigh line. These could serve as a starting point to discover solutions in Rayleigh-stable flows, but the nonlinear stability of Keplerian accretion disks remains to be determined.