# Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

## TL;DR

This study uses numerical simulations to identify three flow regimes in quasi-static magnetoconvection with a vertical magnetic field, revealing a potential 'ultimate' regime characterized by anisotropic, quasi-laminar flow structures and specific heat transport scaling.

## Contribution

The paper characterizes three distinct magnetoconvection regimes at high Chandrasekhar numbers, including a novel 'ultimate' regime with unique flow morphology and scaling properties.

## Key findings

- Identification of three magnetoconvection regimes.
- Discovery of an 'ultimate' regime with anisotropic fluid columns.
- Heat transport scaling independent of Prandtl number in high-Q regimes.

## Abstract

Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^8$ over a broad range of Rayleigh numbers $Ra$. Three magnetoconvection regimes are identified: two of the regimes are magnetically-constrained in the sense that a leading-order balance exists between the Lorentz and buoyancy forces, whereas the third regime is characterized by unbalanced dynamics that is similar to non-magnetic convection. Each regime is distinguished by flow morphology, momentum and heat equation balances, and heat transport behavior. One of the magnetically-constrained regimes appears to represent an `ultimate' magnetoconvection regime in the dual limit of asymptotically-large buoyancy forcing and magnetic field strength; this regime is characterized by an interconnected network of anisotropic, spatially-localized fluid columns aligned with the direction of the imposed magnetic field that remain quasi-laminar despite having large flow speeds. As for non-magnetic convection, heat transport is controlled primarily by the thermal boundary layer. Empirically, the scaling of the heat transport and flow speeds with $Ra$ appear to be independent of the thermal Prandtl number within the magnetically-constrained, high-$Q$ regimes.