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

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.