Regime classification and planform scaling for internally heated mantle convection

Internally heated 3-D mantle convection models in a spherical shell with temperature and pressure dependent viscosity have been performed to provide new insights into the various convection regimes, the transition from steady state convection to time-dependent convection and the associated convection pattern. The analysis of a total of 91 simulations reveals four regime types, i.e., a mobile-lid regime, a sluggish regime, a low-degree regime, and a stagnant-lid regime. The occurrence of these regimes depends on the viscosity contrast and the internal Rayleigh number. The low-degree regime occurs close to the boundary of the stagnant-lid regime in case of temperature dependent viscosity. In case of additional pressure dependence, the range of the low-degree regime is smaller and a narrow range of the sluggish-lid regime exists in the weakly convecting part. Furthermore, the transition to the stagnant-lid regime occurs at a lower viscosity contrast. For the stagnant-lid regime we have derived a scaling law describing the heat transport. Similar scalings could not be obtained for the other regimes as this seems to require also a correlation of the convective pattern with the internal Rayleigh number. Such a relation is only given for the stagnant-lid regime in case of 3D spherical geometry. The stagnant-lid cases in steady state show a minimal possible degree of the convective pattern that is independent on the pressure dependence of viscosity and remains constant until time-dependent convection sets in with increasing Ra. At this stage, the dominant degree of the convective pattern increases with increasing internal Ra but the slope varies with the pressure dependence of the viscosity.