Force Balances and Flow Regimes in MHD Convective Simulations

Strong background magnetic fields inhibit convection, as seen in sunspots, and are responsible for the difference in convective patterns between plage regions and the quiet Sun. The strength of this background field determines how dynamically important the Lorentz force is. It is crucial to the developing theory of magnetoconvection to understand the interplay between the Lorentz and buoyancy forces as the field strength changes, and how this balance affects the dynamics of the flow. In this work, we use Dedalus to study MHD Rayleigh-Bernard convection. We perform a suite of 2D simulations in which the strength of the background magnetic field and the strength of convective driving (quantified by the Chandrasekhar number and the Rayleigh number, respectively) vary by many orders of magnitude. We measure & report the first and second-order force balances in order to understand how magnetically constrained the system is. The degree of magnetic constraint felt by the nonlinear convective solution depends on whether there is a leading-order balance between the Lorentz and buoyancy forces. We quantify regimes in which these simulations exist based on the primary & secondary force balance, and determine scaling laws for the velocity and the induced magnetic field within these regimes.