Periodic Reporting for period 1 - DynMode (Nonlinear astrophysical dynamos: a novel data-driven approach for interscale dynamics)
Reporting period: 2020-09-01 to 2022-08-31
Many astrophysical objects, such as planets, stars, accretion discs and galaxies possess non-decaying magnetic fields. It is widely believed that these magnetic fields are generated through the action of the magnetohydrodynamic dynamo, a complex nonlinear physical process of magnetic field generation by the motion of conductive fluids. This process depends in a non-trivial way on the structure, chemical composition, stage of evolution of the astrophysical object and its overall energy budget; understanding the dynamo would not only help to describe the magnetic field generation in itself, but also to better understand other properties of planets, stars and accretion disks. There are, however, three long-standing problems in dynamo studies: (i) the physical parameters at which dynamo operates are very hard to achieve experimentally, (ii) full-scale numerical dynamo simulations are not feasible due to enormous range of length and time scales in the flow, and (iii) existing numerical models of turbulent flows with millions of degrees of freedom usually give only a very broad qualitative overview of observed interaction between the magnetic and flow fields.
The overall objectives of this project were: to analyze the dynamo data from existing numerical models in various geometries with data-driven methods; to identify and extract spatial patterns (modes) corresponding to dynamically relevant components of the dynamo flow; and to relate the temporal evolution of the spatial components, or modal basis, in data-driven reduced-order models that would describe the nonlinear interactions between magnetic and flow fields.
The overall objectives of this project were: to analyze the dynamo data from existing numerical models in various geometries with data-driven methods; to identify and extract spatial patterns (modes) corresponding to dynamically relevant components of the dynamo flow; and to relate the temporal evolution of the spatial components, or modal basis, in data-driven reduced-order models that would describe the nonlinear interactions between magnetic and flow fields.
During the execution of this project, numerical dynamo data sets were collected in various systems: one-dimensional benchmark dynamo models; helically forced dynamos in Cartesian boxes; convectively driven dynamos in a spherical shell; magnetized shear flow between two co-rotating concentric cylinders. Different modal decomposition methods (Principal Orthogonal Decomposition, Dynamic Mode Decomposition and Hankel Dynamic mode decomposition) were compared against each other on these data sets and coherent components of velocity and magnetic field were extracted for these flows. A benchmark dynamo model featuring small and large scales was developed, and the nonlinear interactions between these scales were investigated using Dynamic Mode Decomposition (DMD). Furthermore, DMD was used to identify the dynamical flow structures related to the transition to chaos in the magnetized rotating shear flow, closely related to the dynamo problem. Nonlinear reduced-order data-driven models were constructed for another one-dimensional but physically relevant dynamo model, highlighting nonlinear interactions between magnetic and velocity fields. These nonlinear models reproduced the supercritical bifurcation scenario in this system and demonstrated robust behaviour even when the parameters of the system were extrapolated. Furthermore, a considerable amount of work has been done towards modal decomposition and reduced-order modelling of transition between strong and weak dynamo branches, a long-standing question in planetary physics.
The dissemination of the results has been achieved through participation in 4 conferences and workshops, and participation in the scientific forums and groups (Astrophysical and Geophysical Fluid dynamics Group, Leeds Institute for Fluid Dynamics, and Women in MHD forum). The results of this work were presented during the INI programme “Frontiers in dynamo theory: from the Earth to the stars”, and received positive feedback from the experts in the community. Part of these results is currently under review in the journal “Philosophical Transactions of the Royal Society A”, and another part is being prepared for publication.
The dissemination of the results has been achieved through participation in 4 conferences and workshops, and participation in the scientific forums and groups (Astrophysical and Geophysical Fluid dynamics Group, Leeds Institute for Fluid Dynamics, and Women in MHD forum). The results of this work were presented during the INI programme “Frontiers in dynamo theory: from the Earth to the stars”, and received positive feedback from the experts in the community. Part of these results is currently under review in the journal “Philosophical Transactions of the Royal Society A”, and another part is being prepared for publication.
The project has brought and promoted data-driven methods of modal decomposition and model reduction in the dynamo research; most of the data-driven techniques used in this project were applied to the dynamo flows successfully for the first time. Similarly, Dynamic Mode Decomposition was used as a diagnostic tool to identify the key structures related to the transition to turbulence in a magnetohydrodynamic flow. A large database of diverse dynamo flows was collected and can be further used for analysis; the results of the work will be of interest not only specifically to the dynamo community, but to a wide range of researchers in fluid dynamics.