  Adding moving boundaries to convective fluids is known to result in
nontrivial and surprising dynamics, leading to spectacular geoformations
ranging from the kilometer-scale karst terrains to the planetary-scale plate
tectonics. On one hand, the moving solid alters the surrounding flow field, but
on the other hand, the flow modifies the motion and shape of the solid. This
leads to a two-way coupling that is significant in the study of fluid-structure
interactions and in the understanding of geomorphologies. In this work, we
investigate the coupling between a floating plate and the convective fluid
below it. Through numerical experiments, we show the motion of this plate is
driven by the flow beneath. However the flow structure is also modified by the
presence of this plate, leading to the "thermal blanket" effect where the
trapped heat beneath the plate results in buoyant and upwelling flows that in
turn push the plate away. By analyzing this two-way coupling between moving
boundary and fluid, we are able to capture the dynamical behaviors of this
plate through a low-dimensional stochastic model. Geophysically, the thermal
blanket effect is believed to drive the continental drift, therefore
understanding this mechanism has significance beyond fluid dynamics.
