On the Dynamics of Plate Tectonics: Multiple Solutions, the Influence of Water, and Thermal Evolution

Abstract

An analytic boundary layer model for thermal convection with a finite-strength plate and depth-dependent viscosity is developed. The model includes a specific energy balance for the lithosphere and accounts for coupling between the plate and underlying mantle. Multiple solutions are possible with three solution branches representing three distinct modes of thermal convection. One branch corresponds to the classic boundary layer solution for active lid plate tectonics while two new branches represent solutions for sluggish lid convection. The model is compared to numerical simulations with highly temperature dependent viscosity and is able to predict both the type of convection (active, sluggish, or stagnant lid) as well as the presence of single and multiple solution regimes. The existence of multiple solutions suggests that the mode of planetary convection may be history dependent. The dependence of mantle viscosity on temperature and water concentration is found to introduce a strong dynamic feedback with plate tectonics. A dimensionless parameter is defined to quantitatively evaluate the relative strength of this feedback and demonstrates that water and heat transport may be equally important in controlling present-day platemantle dynamics for the Earth. A simple parameterized evolution model illustrates the feedback and agrees well with our analytic results. This suggests that a simple relationship may exist between the rate of change of water concentration and the rate of change of temperature in the mantle. This study concludes by investigating the possibility of a magnetic field dynamo in early solar system planetesimals. The thermal evolution of planetesimals is modeled by considering melting, core formation, and the onset of mantle convection and then employing thermal boundary layer theory for stagnant lid convection (if possible) to determine the cooling rate of the body. We assess the presence, strength and duration of a dynamo for a range of planetesimal sizes and other parameters. We find that a minimum radius of O(500) km is required for a thermally driven dynamo of duration O(10) My. The dependence of the results on model parameters is made explicit through the derivation of an analytic solution.