We present an analytic boundary layer model for thermal convection with a finite-strength plate and depth-dependent viscosity. The model permits solutions in which convective flow rates in the mantle exceed the plate velocity. The energy balance equations for the lithosphere and convective cell are distinct and the model yields the plate velocity, plate thickness and heat flow, as well as the laterally averaged horizontal flow profile for a convective cell.
We demonstrate, by inspection of the lithospheric energy balance, that the dominant plate driving force depends not only on the material properties of the mantle and lithosphere, but also on the velocity of the plate. Multiple solutions are possible with three solution branches for the plate velocity representing three distinct modes of thermal convection. The branch of solutions with the largest plate velocity corresponds to the classic boundary layer solution, with a plate velocity approximately equal to the maximum mantle velocity. This branch reproduces the classic convective scaling laws for an isoviscous fluid and its dynamics are controlled by the mantle material properties. The branch of solutions with intermediate plate velocity represents a convective cell with a sluggish-lid and a plate velocity that is less than the underlying mantle velocity. The dynamics for this solution branch depend on the material properties of both the mantle and the lithosphere. Finally, the lower branch of solutions for the plate velocity yields a convective solution in which the plate velocity is determined entirely by the local dynamics of a thick and strong (relative to the mantle) lithosphere. The dynamics of this solution branch are independent of the material properties of the mantle and depend entirely on the properties of the lithosphere.
The introduction of an asthenosphere or low viscosity layer (LVL) beneath the plate can significantly alter the dynamics of the system by affecting plate–mantle coupling. Lowering the LVL viscosity, relative to the lower mantle, can promote plate motion by providing a lubricating layer. However, a very low viscosity LVL beneath a strong plate can decouple plate and mantle and inhibit plate motion, producing a solution with a slow moving plate and a channelized flow in the LVL. Thus, a LVL can sometimes inhibit rather than promote plate tectonics.