On the dynamics of plate tectonics

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.