PI: Andrew Hillier
The project, dp050 Solar Instabilities, in the year 2025, focused on one of fundamental instabilities in solar physics, magnetic Rayleigh Taylor instability. The instability is also well known to occur across diverse astrophysical and laboratory system. Unravelling the role of magnetic field on the instability evolution and dynamics demands a more focused approach. Hence, in this project we considered a simplified problem of simulating MRTI under the approximations of incompressible, fully ionized plasma using a highly accurate spectral solver code, Dedalus.
Despite it’s ubiquity, a problem that remained unresolved so far, is the nature of MRTI evolution. To address this fundamental question, we developed analytical framework which showed that the MRTI is not always self-similar, but only achieves self-similar state as the magnetic field term decays inversely with time and when magnetic field is dominated by other non-linear terms. These results contradict the years of assumption, that MRTI is always self-similar.
To corroborate the analytical results, we simulated MRTI in a 3D domain, using a three stage fourth order Runge Kutta Scheme. The scheme while computationally intensive was necessary to get accurate results. Therefore, we used the COSMA (Compute Optimised System for Memory-intensive Algorithms) hosted by the Institute for Computational Cosmology (ICC) at Durham University. We ran the simulations at varying magnetic field strengths to perform robust test of the analytical theory conclusions. The numerical simulations showed that the MRTI indeed is conditionally self-similar, with magnetic field decaying inversely with time.
Further, the numerical simulations were used to develop a deeper understanding of how and why the non-linear growth of MRTI changes with magnetic field strength. The study found that the increasing magnetic field strength increases turbulence, turbulent magnetic energy, and reduces small scale structures, turbulent kinetic energy and energy dissipation. These lead to faster growth of instability for high magnetic field strength. Leveraging the different magnetic field strength cases, scaling laws were established for energy dissipation and energy partition between magnetic and kinetic energies with imposed magnetic field strength.
Figure showing the 3D density contours (left) and 2D current contours (on a mid plane) (right) at two different magnetic field strengths: (top) weak magnetic field (bottom) strong magnetic field.
