Thermal Convection with a Strong Vertical Magnetic Field

The fluid outer core of the earth and many other planetary interiors possess large scale magnetic fields. These magnetic fields can change the dynamics of the flow significantly, thus in order to understand the mechanism of dynamo, it is important to look into the physics of magnetoconvection with strong magnetic fields. Here, we consider the extreme cases of small magnetic Prandtl number magnetoconvection with an imposed vertical magnetic field. We applied a quasi-static incompressible magneto-hydrodynamic model, and a set of direct numerical simulations is conducted in a Cartesian plane layer geometry. Three regimes of flow are observed when we increasing the Rayleigh number Ra with fixed Chandrasekhar number Q, characterized by different flow structures and Nu-Ra scaling. In the first one, the boundary layer is not well formed and there is still a mean temperature gradient at mid-plane. In the second regime the interior of the flow becomes isothermal, and the Nu-Ra scaling agrees with marginal stability analysis, indicating that the convection is controlled by the boundary layer. At even higher Ra, the inertia takes the dominant balance over Lorenz force, resulting in a Nu-Ra scaling close to non-magnetic model. The distinguished changes of the dominant terms in the equations and the contribution of ohmic dissipation and viscous dissipation are analyzed. A reversed temperature profile occurs in the second regime, which associated with a stable plume structure, suggesting an efficient way of heat transfer. The result of this magnetoconvection research reveals the role magnetic field plays on natural dynamo.