The Elbert range of magnetostrophic convection. II. Comparing linear theory to nonlinear low- <i>Rm</i> simulations

The magnetostrophic dynamo hypothesis has greatly influenced planetary dynamo research. Many magnetostrophic dynamo theories are founded upon the linear stability analysis by Chandrasekhar and Elbert, and by the canonical laboratory photographs taken by Nakagawa that show a significant enlargement of the convective flow scales in the magnetostrophic regime of liquid metal rotating magnetoconvection (RMC). We test whether these linear predictions are relevant for the nonlinear RMC system by exploring the five possible regimes using direct numerical simulations of RMC in the low magnetic Reynolds number quasi-static approximation. We map out the heat and momentum transport in these regimes, look at the flow structures and focus especially on the length scales. We have also included numerical counterparts of Nakagawa’s experiments and our results show an excellent agreement with three of these cases and linear theory. However, agreement with Nakagawa is not found in the magnetostrophic case: no enlargement of scales is observed, but still in good agreement with linear theory. Oscillatory bulk modes dominate all the RMC cases in which they exist, thus, suggesting that oscillatory convective flows may dominate all the other convective modes in planetary cores and may provide the motions that primarily generate planetary dynamo action.