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We present results from an asymptotic magnetohydrodynamic model that issuited for studying the rapidly rotating, low viscosity regime typical of theelectrically conducting fluid interiors of planets and stars. We show that thepresence of sufficiently strong magnetic fields prevents the formation oflarge-scale vortices and saturates the inverse cascade at a finitelength-scale. This saturation corresponds to an equilibrated state in which theenergetics of the depth-averaged flows are characterized by a balance ofconvective power input and ohmic dissipation. A quantitative criteriadelineating the transition between finite-size flows and domain-filling(large-scale) vortices in electrically conducting fluids is found. By makinguse of the inferred and observed properties of planetary interiors, our resultssuggest that convection-driven large-scale vortices do not form in theelectrically conducting regions of many bodies.

Magnetic quenching of the inverse cascade in rapidly rotating convective turbulence