The project, going beyond the state-of-the-art, aimed at clarifying these issues by in-depth investigation of the dynamics of MRI in disks – its linear growth, nonlinear saturation and energetic balances in the resulting turbulence, associated transport and dynamo action under different physical conditions in disks, building on my previous findings in shear flow turbulence theory. First of all, these are the new concepts of shear-induced spectral anisotropy, nonlinear transverse cascade and vital area of turbulence, which I elaborated and which lie at the heart of sustaining dynamics of turbulence in shear flows, whose special case is MRI-turbulence in disks. This new approach consists in a combination of simulations of equations of magnetohydrodynamics and, on their basis, a detailed analysis of the dynamical process in Fourier space, where much richer dynamics unfolds than that in physical (coordinate) space. It has offered a deeper understanding of the sustenance and evolution of MRI-turbulence in disks and, importantly, enabled further progress in the resolution of the above three main issues, which, however, are not accessible to an analysis in physical space, as done before in most studies. Thus, with this new approach, we have gone beyond the state-of-the-art in MRI studies, providing a new perspective on MRI-turbulence dynamics that contributes to clarification of the main outstanding issues still persisting due to conservative approaches used so far.
The project will have a wide impact, since the elaborated methods and obtained results are of interdisciplinary value that can be of interest to different (e.g. hydrodynamical, plasma physics, geophysical, etc.) communities studying shear flow turbulence. The new concepts and processes studied in the project, such as anisotropic spectra and transverse cascade, are in fact generic to any shear flow in nature, industry and lab and will form a basis for new studies in shear flow turbulence in Fluid Dynamics, Plasma Physics, Geophysics, Space Physics, etc. The main goal of the project was to study sustaining dynamics of turbulence in disks, which are special cases of shear flows, and to show the role of the transverse cascade therein. In this way, the project has also contributed to an establishment of the transverse cascade as a necessary alternative to usual inverse/direct cascades in shear flows. The transverse cascade calls for revision of these well-known cascade processes of Kolmogorov’s theory of turbulence in relation to shear flows.
