MHDSSP: Self-sustaining processes and edge states in magnetohydrodynamic flows subject to rotation and shear

该项目旨在研究天体物理盘中的自持过程(SSP)，利用流体力学中发展起来的概念和技术来理解层流-湍流转变(LTT)。SSP在壁面边界流动的LTT中的重要性早已被认识到。这些过程通常由一系列轧辊组成，这些轧辊驱动流向条纹，这些条纹破坏稳定并反馈到轧辊上。这种过程与磁流体动力(MHD)流动的发电机问题中遇到的问题密切相关，其中极向磁场产生环向磁场，该磁场对磁致旋转不稳定性(MRI)是不稳定的，从而能够重新产生极向场。与流体力学情况相比，MHD中的相应过程知之甚少。具体来说，(1)旋转影响下MRI模式对极向场的反馈特性，以及(2)自持状态的性质等关键问题没有得到解决。同时，在天体物理学中，关于(3)数值模拟中有限大小的区域对发电机过程的影响的争论由来已久。该项目包含六个工作包，力求通过分析和数值方法相结合来解决这些悬而未决的问题。首先，将推导出MHD中SSP的渐近理论，该理论能够预测大雷诺数下的自持状态。然后，这一理论将被验证，并与数值计算的处于层状和湍流边缘的自持状态进行比较。最后，研究了磁区大小对这些态的影响。所提出的研究不仅有望极大地促进我们对问题(1)-(3)的理解，为旋转剪切流中发电机的启动带来新的知识，而且还有助于将动力系统理论的最新观点介绍给MHD和天体物理界。

The project aims at investigating self-sustaining processes (SSPs) in astrophysical discs, using concepts and techniques developed in fluid mechanics to understand laminar-turbulent transition (LTT). The importance of SSPs in LTT of wall-bounded flows has long been recognised. These processes typically consist of an array of rolls that drive streamwise streaks, which destabilise and feed back on the rolls. Such processes are closely related to those encountered in dynamo problems of magnetohydrodynamic (MHD) flows, where a poloidal magnetic field generates a toroidal magnetic field, which is unstable to the magnetorotational instability (MRI), and thus capable of re-generating the poloidal field. In contrast to the hydrodynamic case, little is known about the corresponding process in MHD. Specifically, key questions such as (1) the character of the feedback from the MRI-modes to the poloidal field under the influence of rotation, and (2) the nature of the self-sustaining states are unsolved. Meanwhile, there is a long-standing debate within astrophysics regarding (3) the effects of finite-size domains in numerical simulations on dynamo processes like the one outlined above. The project contains six work packages and seeks to address these open questions through a combination of both analytical and numerical methods. First, an asymptotic theory for SSPs in MHD will be derived that enables self-sustaining states at large Reynolds numbers to be predicted. Then, this theory will be validated and compared against numerically computed self-sustaining states on the verge between laminarity and turbulence. Finally, the influence of the domain size on such states will be studied. The proposed research is not only expected to significantly advance our understanding of the issues (1)-(3) and bring new knowledge to the onset of dynamos in rotating shear flows, but also serve to introduce recent ideas from the dynamical systems theory to the MHD and the astrophysics community.