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

MHDSSP：受到旋转和剪切作用的磁流体动力流中的自持过程和边缘状态

• 批准号: EP/Y029194/1
• 负责人: Gordon Ogilvie
• 金额: $ 23.84万
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY029194%2F1
• 关键词: MHDSSP; Self; sustaining; processes; edge

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.

该项目旨在研究天体物理盘中的自维持过程（SSP），利用流体力学中开发的概念和技术来理解层流-湍流转变（LTT）。 SSP 在壁面流动 LTT 中的重要性早已被认识到。这些过程通常由一系列辊子组成，这些辊子驱动流向条纹，这些条纹会破坏辊子的稳定性并反馈到辊子上。这些过程与磁流体动力学（MHD）流的发电机问题密切相关，其中极向磁场产生环形磁场，该磁场对磁旋转不稳定性（MRI）不稳定，因此能够重新生成极向场。与流体动力学情况相反，人们对 MHD 中的相应过程知之甚少。具体来说，诸如（1）在旋转影响下从 MRI 模式到极向场的反馈的特征，以及（2）自维持状态的性质等关键问题尚未解决。与此同时，天体物理学界对于（3）有限尺寸域在数值模拟中对上述发电机过程的影响存在着长期的争论。该项目包含六个工作包，旨在通过分析方法和数值方法的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，该理论将得到验证，并与数值计算的层流和湍流边缘的自持状态进行比较。最后，将研究域大小对此类状态的影响。所提出的研究不仅有望显着增进我们对问题（1）-（3）的理解，并为旋转剪切流中发电机的产生带来新的知识，而且有助于将动力系统理论的最新思想引入到MHD 和天体物理学界。