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Direct numerical simulations are performed to study turbulent Rayleigh–B ́enard convection in a vertical cylindrical cavity exposed to a uniform axial magnetic field. Flows at high Hartmann and Rayleigh numbers are considered. The calculations reveal that, similarly to the behavior observed in Rayleigh–Benard convection with strong rotation, flows under a strong magnetic field develop a central vortex, whereas the heat transfer is suppressed. 

Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh–Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number $0.025$ and Rayleigh and Hartmann numbers up to $10^{9}$ and $1400$ , respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh–Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.