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

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 behaviour. 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.