Adrian Lenardic

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, https://doi.org/10.1111/j.1365-246X.2011.05254.x ) 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.