concept

Rayleigh number

The dimensionless number that decides whether a layer heated from below overturns or merely conducts. It puts buoyancy on top — density, gravity, thermal expansion, the temperature drop, and the layer thickness cubed — and divides by what resists flow: viscosity and thermal diffusivity. Below a threshold of order a few hundred, nothing moves. Earth's mantle runs at roughly 10⁶–10⁸, which is far past it. Note the thickness enters cubed: for the same rock, a thicker layer convects much more readily.