Scaling of plume formation in strongly temperature-dependent viscosity fluids: Application to core-mantle boundary

At large viscosity contrasts across the thermal boundary layer at the core-mantle boundary formation of plumes occurs in several steps. First, a conductive thermal boundary layer starts growing from the core-mantle boundary. Then, a small-scale convection develops within the boundary layer itself. Eventually the convecting boundary layer becomes unstable as a whole and generates a plume. Although the instability of the convective boundary layer was studied by various workers, there are no scaling laws for this process. We develop a scaling theory for plume formation in strongly temperature-dependent fluids using an analogy with Rayleigh-Taylor instability in rheologically stratified fluids (Canright and Morris, 1993; Ribe and de Valpine, 1994) and a scaling theory for small-scale convection in the thermal boundary layer (Solomatov and Moresi, 2002). We perform systematic numerical simulations using the finite element code CITCOM and find a good agreement with the theory. The theory predicts the growth rate of large-scale instability, the critical thickness of the convecting boundary layer, the spacing between plumes and the frequency of plume formation. The theory suggests that the number of plumes is very small, on the order of unity, while the time interval between plume formation is large, on the order of one billion years. This implies that this mechanism is unlikely to be responsible for plume formation on Earth. On the other hand, this can explain superplumes in the past history of the Earth and formation of one large upwelling on Mars.