Effects of kinematic and magnetic boundary conditions on the dynamics of convection-driven plane layer dynamos

Abstract

Rapidly rotating convection-driven dynamos are investigated under different kinematic and magnetic boundary conditions using DNS. At a fixed rotation rate, represented by the Ekman number $E=5\times 10^{-7}$, the thermal forcing is varied from 2 to 20 times its value at the onset of convection ($\mathcal{R}=Ra/R{a}_c=2-20$), keeping the fluid properties constant ($Pr=P{r}_m=1$). The statistical behavior, force balance and heat transport characteristics of the dynamos depend on boundary conditions that dictate both boundary layer and the interior dynamics. At a fixed thermal forcing ($\mathcal{R}=3$), the Ekman plumes in the presence of viscous boundary layers lead to energetic vortices that result in higher enstrophy and kinetic helicity with no-slip boundaries compared to free-slip boundaries. The structure and strength of the magnetic field are also dictated by the boundary conditions. Though the leading order force balance remains geostrophic, Lorentz force dominates inside the thermal boundary layer with no-slip, electrically conducting walls. Here, the Lorentz work term in the turbulent kinetic energy budget is found to have components that exchange energy from the velocity field to the magnetic field, and vice-versa. However, with no-slip, insulated walls, all Lorentz work components perform unidirectional energy transfer to produce magnetic energy from the kinetic energy of the fluid. The heat transfer enhancement in dynamos, compared to non-magnetic rotating convection, exhibits a peak in the range $\mathcal{R}=3-5$. For free-slip conditions, dynamo action may alter the heat transport by suppressing the formation of large-scale vortices. However, the highest heat transfer enhancement occurs when the boundaries are no-slip, electrically conducting walls.

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