A toy model of plate tectonics

Observing the presence of marine fossils in the mountains, Leonardo da Vinci was one of the first scientists who noticed the incessant geological movements of our planet. We now know that the continents do not stay in place and instead undergo tectonic motions, and thermal convection in Earth's mantle is believed to be the driving force of these motions. How does mantle convection couple to the continental drift? Does the moving continent affect the mantle motion beneath it? We address these questions through a simple fluid-structure interaction model, where a simple and efficient spectral solver reveals many geological-like events such as the divergence and convergence of continents and the periodic motion of Wilson cycles. These results are consistent with the lab-scale experiments of Zhang and Zhong (2007), and we hope that such models can shed light on the fluid mechanical origin of plate tectonics.