Earth's mantle is not solid rock — over geological timescales it flows like an incredibly viscous fluid. Heat from the iron core warms the mantle from below while the cool crust sits on top. This temperature difference drives Rayleigh-Bénard convection: hot material becomes less dense and rises; cold material sinks. The result is a set of slowly overturning convection cells that carry heat to the surface and push tectonic plates sideways.
The model solves the 2D Boussinesq equations in vorticity-streamfunction form using finite differences on a 256 × 128 grid. The dimensionless Rayleigh number Ra sets the ratio of buoyancy forces to viscous dissipation. Below Ra ≈ 10³ the flow is purely conductive; above that convection cells appear; above 10⁵ the flow becomes time-dependent and complex.
The mantle convects on a timescale of tens of millions of years — a complete overturn takes roughly 100 million years. Yet in this simulation you can watch the same physics play out in seconds. The Hawaiian island chain was formed as the Pacific plate drifted over a mantle plume (a localised hot upwelling) at about 9 cm per year — roughly the speed your fingernails grow.