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.
