The mantle undergoes slow viscous convection driven by internal heat generation (radioactive decay) and cooling at the surface, transporting heat and material over geologic timescales. Convection is modeled as Rayleigh-Bénard convection modified by pressure-dependent viscosity, internal heating, and phase transitions; patterns range from laminar (whole-mantle) to plume-dominated depending on Rayleigh number. Mantle convection drives plate motion, creates spreading ridges and subduction zones, and generates plume volcanism; seismic tomography, geochemistry, and numerical models illuminate the vigor and pattern of mantle flow.
From your work on rock rheology, you know that mantle rock, while solid on human timescales, behaves as a viscous fluid when stress is applied slowly over millions of years. This is the key to understanding mantle convection: the mantle is not liquid, but it flows. The question is what drives that flow and how it shapes the planet's surface.
The engine is heat. Earth's interior is hot for two reasons: primordial heat trapped during the planet's violent formation, and ongoing radioactive decay of isotopes like uranium-238, thorium-232, and potassium-40. Heat conducts upward through rock far too slowly to account for the observed surface heat flux — convection must be doing most of the transport. Hot, less-dense material at depth becomes buoyant, rises slowly toward the surface (taking perhaps 100 million years to traverse the mantle), loses heat by conduction, becomes denser, and sinks again. The result is a slow, planet-scale overturn.
From your study of Rayleigh-Bénard convection, you know that whether a fluid layer actually convects depends on the balance between buoyancy (which drives flow) and viscosity and thermal diffusivity (which resist it). This balance is captured by the Rayleigh number. Earth's mantle has a very high Rayleigh number — roughly 10^7 to 10^8 — meaning buoyancy wins decisively and convection is vigorous despite the mantle's high viscosity. The exact pattern of convection (whole-mantle vs. layered, diffuse upwelling vs. focused plumes) is modified by phase transitions in the transition zone around 660 km depth and by pressure-dependent viscosity, making mantle dynamics far richer than simple Rayleigh-Bénard cells.
The surface expression of this deep flow is plate tectonics. Where hot mantle material rises and spreads laterally, oceanic crust rifts apart to form mid-ocean ridges. Where old, cold, dense oceanic plates sink back into the mantle, subduction zones form. Isolated hot upwellings — mantle plumes — punch through the overlying plate to produce hotspot volcanism like Hawaii. The speeds are glacial by human standards (centimeters per year) but immense on geologic timescales.
Because the mantle is inaccessible, we infer its structure indirectly. Seismic tomography — using seismic waves from earthquakes as a kind of CT scan — reveals cold, fast-wave-velocity slabs plunging into the mantle and hot, slow-velocity zones beneath ridges and hotspots. Geochemistry of lavas samples different mantle reservoirs, constraining mixing and flow histories. Numerical models, informed by laboratory experiments on rock rheology, simulate the flow and are tested against these observations. Together they give us a picture of a planet whose surface is moved by forces rooted hundreds of kilometers below it.