Modes of Mantle Convection, Their Stability, and What Controls Their Existence

The motion of Earth's tectonic plates is the surface expression of mantle convection beneath. Analytical convection models have attempted to relate observables, such as plate velocities and surface heat flow, with the thermo-mechanical state of the mantle, and remain deeply influential in global geophysics. While such models tend to focus on describing the mantle's behavior today, there is evidence that suggests they may not be the best description for an earlier, hotter mantle. Early in Earth's history, higher temperatures may have led to different convective regimes that include active-lid (today's form of convection), sluggish-lid, and stagnant-lid convection. In this study, we adopt and extend the analytical theory laid out by Crowley & O'Connell (2012, ) that self-consistently characterizes the first two of these convection regimes. For a given thermo-mechanical state, the theory predicts one to multiple solutions that each represent distinct modes of mantle convection. Here, we derive new scaling laws that connect these modes to the mantle's Rayleigh number and identify a new fundamental, dimensionless number, which we term the O'Connell number (named after Richard "Rick" J. O'Connell (1941-2015)), that describes a plate's resistance in context of the overall convection of the system. In addition, we identify two key bifurcations that bracket the Rayleigh-O'Connell number space within which multiple solutions may exist. Finally, we remove the assumption of steady-state in their original framework in order to perform a linear stability analysis to characterize the relative stability of each convection mode. Earth's tectonic plates presently take part in the motion of the mantle in the subsurface via a process known as convection. Plates are created at mid-ocean spreading ridges and destroyed at subduction zones, and move at approximately the same speeds as the mantle. In the past when the mantle was hotter, it is unclear how the surface plates and the subsurface mantle interacted: classical models indicate that with higher temperatures and increased vigor of convection, plates are expected to move faster. The geological record indicates that plate velocities in the past were similar to today's. The need to reconcile the geologic record with models of mantle convection has driven the scientific community to revise these models. One of these revisions, Crowley and O'Connell (2012, ), finds that for a hotter Earth, there are multiple ways in which the mantle and plate may move relative to each other. In some cases, coupling between the cold surface and the hot mantle is reduced, and plates move slowly while the mantle moves much faster. We return to their model to investigate the physics that causes these distinct plate/mantle relationships, derive mathematical descriptions for this behavior, and explore the conditions for their existence and likelihood. We derive new scaling laws for the sluggish-lid mantle convection modes with the aid of a new non-dimensional numberThe stability of these modes is established, which reveals that one of these regimes is thermodynamically stableWe construct a phase space regime diagram for the permissible mantle convective modes