Heat Flow Scaling of Convection with Damage Theory and the Onset of Plate Tectonics

Damage theory, which uses the observation that mineral grains tend to shrink under deformation, making the material weaker, and grow in the absence of applied stress, making the material stronger, has been proposed as a possible mechanism for shear localization in the Earth. A theoretical description of this rheology for continuum models has been developed, and it has been shown capable of producing a plate-like style of convection in 2-D convection models with a low (4-6 order of magnitude) viscosity contrast due to temperature dependence. This rheology utilizes a temperature and grain-size dependent viscosity, where grain-size in turn depends on deformational work and temperature. This results from assuming that in a statistical distribution of grain sizes, dislocation creep dominates in the larger grains, decreasing their size through dynamic recrystallization, while smaller grains deform in a diffusion creep regime. The bulk viscosity of the material is then controled by its weakest component, the small grains deforming by grain-size sensitive diffusion creep. Grains grow faster at higher temperatures, tending to increase viscosity in competition with the effect from thermally activated creep processes. This competition can therefore cause convection on the Earth to undergo changes in convective style due to its thermal evolution. A simple thermal evolution model assuming that the Nusselt number (Nu) scales as the Rayleigh number (Ra) to the 1/3 shows that two convection states, a stagnant surface and mobile surface, exist depending on material properties and thermal conditions. However, a heat flow scaling law for our more complicated viscosity model is dependent on more non-dimensional parameters than Ra, and perhaps completely different from the classical law for isoviscous convection. An investigation of the heat flow scaling law through 2-D numerical convection experiments is presented, as well as an extension of the regime diagram to higher viscosity contrasts. These results have important implications for possible shifts in tectonic regimes due to the Earth’s thermal evolution.