Unifying heat transport model for the transition between buoyancy-dominated and Lorentz-force-dominated regimes in quasistatic magnetoconvection

In magnetoconvection, the flow is driven by buoyancy and Lorentz forces that distort the convective flow structure in the presence of a magnetic field. The different flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct scaling relations of the total heat flux versus the strength of buoyancy and electromagnetic forces. Here, we propose a theoretical model for the transition between these two regimes for the case of a quasistatic vertical magnetic field applied to a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. We derive the relation between the scaling exponents in these two regimes and also the scaling of the onset of the transition. The theory is supported by our DNS and data from the literature.