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.

该项目旨在使用流体力学中开发的概念和技术来研究天体物理盘中的自我维持过程（SSP），以了解层流扰动的过渡（LTT）。长期以来，已经认识到SSP中SSP在壁挂式流量的LTT中的重要性。这些过程通常由一系列滚动的滚动，这些掷骰驱动流式条纹，这些条纹破坏了稳定并反馈在滚动上。此类过程与磁流失动力学（MHD）流的发电机问题遇到的过程密切相关，其中多磁场会产生环形磁场，该磁场对磁化磁不稳定（MRI）不稳定，因此能够重新生成多核场。与流体动力学病例相反，对MHD中的相应过程知之甚少。具体而言，诸如（1）在旋转影响下从MRI模型到多型磁场的反馈的特征以及（2）尚未解决自我维持状态的性质。同时，在天体物理学中，关于（3）数值模拟中有限尺寸域对上述发电机过程的影响。该项目包含六个工作包，并试图通过分析和数值方法的结合来解决这些开放问题。首先，将得出MHD中SSP的渐近理论，该理论可以预测大雷诺数的自我维持状态。然后，该理论将得到验证并与数字计算的自我维持状态进行比较。最后，将研究域大小对此类状态的影响。拟议的研究不仅预计会大大提高我们对问题（1） - （3）的理解，并在旋转剪切流中为Dynamos发作带来新知识，而且还可以介绍从动力学系统理论到MHD和天体物理学界的最新思想。