Scaling of plate-tectonic convection with pseudoplastic rheology

TL;DR

This paper develops scaling laws for plate-tectonic convection considering pseudoplastic rheology and temperature-dependent viscosity, linking mantle dynamics to surface heat flux and the effects of surface water on tectonic activity.

Contribution

It introduces a new scaling framework for plate-tectonic convection that incorporates pseudoplastic rheology and depth-dependent viscosity effects.

Findings

Heat-flow scaling depends on Rayleigh number and lithospheric viscosity contrast.

Critical viscosity contrast for transition to stagnant-lid convection scales with Rayleigh number.

Surface water reduces friction, making plate tectonics plausible throughout Earth's history.

Abstract

The scaling of plate-tectonic convection is investigated by simulating thermal convection with pseudoplastic rheology and strongly temperature-dependent viscosity. The effect of mantle melting is also explored with additional depth-dependent viscosity. Heat-flow scaling can be constructed with only two parameters, the internal Rayleigh number and the lithospheric viscosity contrast, the latter of which is determined entirely by rheological properties. The critical viscosity contrast for the transition between plate-tectonic and stagnant-lid convection is found to be proportional to the square root of the internal Rayleigh number. The relation between mantle temperature and surface heat flux on Earth is discussed on the basis of these scaling laws, and the inverse relationship between them, as previously suggested from the consideration of global energy balance, is confirmed by this fully dynamic approach. In the presence of surface water to reduce the effective friction coefficient, the operation of plate tectonics is suggested to be plausible throughout the Earth history.