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Numerical experiments of convection with grain-damage are used to developscaling laws for convective heat flow, mantle velocity, and plate velocityacross the stagnant lid and plate-tectonic regimes. Three main cases arepresented in order of increasing complexity: a simple case wherein viscosity isonly dependent on grainsize, a case where viscosity depends on temperature andgrainsize, and finally a case where viscosity is temperature and grainsizesensitive, and the grain-growth (or healing) is also temperature sensitive. Inall cases, convection with grain-damage scales differently than Newtonianconvection due to the effects of grain-damage. For the fully realistic case,numerical results show stagnant lid convection, fully mobilized convection thatresembles the temperature-independent viscosity case, and partially mobile ortransitional convection, depending on damage to healing ratio, Rayleigh number,and the activation energies for viscosity and healing. Applying our scalinglaws for the fully realistic case to Earth and Venus we demonstrate thatincreasing surface temperature dramatically decreases plate speed and heatflow, essentially shutting down plate tectonics, due to increased healing inlithospheric shear zones, as proposed previously. Contrary to many previousstudies, the transitional regime between the stagnant lid and fully mobilizedregimes is large, and the transition from stagnant lid to mobile convection isgradual and continuous. Thus planets could exhibit a full range of surfacemobility, as opposed to the bimodal distribution of fully mobile lid planetsand stagnant lid planets that is typically assumed.

Scaling Laws for Convection with Temperature-dependent Viscosity and Grain-damage