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

TL;DR

This paper develops scaling laws for convection with grain-damage considering temperature-dependent viscosity, revealing how surface temperature influences planetary tectonics and demonstrating a continuum of surface mobility regimes.

Contribution

It introduces new scaling laws for grain-damage convection that incorporate temperature dependence, expanding understanding of planetary mantle dynamics.

Findings

Increasing surface temperature reduces plate speed and heat flow.

Transitional convection regimes are larger and more gradual than previously thought.

Planets can exhibit a continuum of surface mobility states.

Abstract

Numerical experiments of convection with grain-damage are used to develop scaling laws for convective heat flow, mantle velocity, and plate velocity across the stagnant lid and plate-tectonic regimes. Three main cases are presented in order of increasing complexity: a simple case wherein viscosity is only dependent on grainsize, a case where viscosity depends on temperature and grainsize, and finally a case where viscosity is temperature and grainsize sensitive, and the grain-growth (or healing) is also temperature sensitive. In all cases, convection with grain-damage scales differently than Newtonian convection due to the effects of grain-damage. For the fully realistic case, numerical results show stagnant lid convection, fully mobilized convection that resembles the temperature-independent viscosity case, and partially mobile or transitional convection, depending on damage to healing ratio, Rayleigh number, and the activation energies for viscosity and healing. Applying our scaling laws for the fully realistic case to Earth and Venus we demonstrate that increasing surface temperature dramatically decreases plate speed and heat flow, essentially shutting down plate tectonics, due to increased healing in lithospheric shear zones, as proposed previously. Contrary to many previous studies, the transitional regime between the stagnant lid and fully mobilized regimes is large, and the transition from stagnant lid to mobile convection is gradual and continuous. Thus planets could exhibit a full range of surface mobility, as opposed to the bimodal distribution of fully mobile lid planets and stagnant lid planets that is typically assumed.