Thermal Convection in Earth's Mantle
Earth's mantle, despite being solid rock, flows like an extremely viscous fluid over geological time scales. Heat from the core and radioactive decay creates buoyancy forces that drive convection: hot, less-dense material rises while cold, dense material sinks. This process transports over 70% of Earth's internal heat to the surface and drives plate tectonics.
The Rayleigh Number
The Rayleigh number is the key dimensionless parameter governing convection. It quantifies the competition between thermal buoyancy (promoting flow) and viscous resistance plus thermal diffusion (inhibiting flow). When Ra exceeds a critical value, convection initiates as steady rolls. At higher Ra values, the flow becomes increasingly complex, time-dependent, and eventually chaotic.
Boundary Layers and Plumes
Convection in the mantle develops thin thermal boundary layers at the top (lithosphere) and bottom (D" layer above the core-mantle boundary). These boundary layers can become gravitationally unstable, spawning cold downwellings (subducting slabs) from the top and hot upwellings (mantle plumes) from the bottom. The asymmetry between these features reflects the role of internal heating from radioactive decay.
Heat Flow and Nusselt Number
The Nusselt number compares actual convective heat transport to what pure conduction would achieve. For mantle-like Rayleigh numbers, Nu ~ Ra^(1/3), meaning convection enhances heat loss by an order of magnitude. Earth's mean surface heat flow of ~87 mW/m² reflects this convective enhancement, with higher values at mid-ocean ridges and lower values in continental shield regions.