What is Rayleigh number?

For a fluid layer of thickness $d$, density $\rho$, thermal expansion coefficient $\alpha$, thermal diffusivity $\kappa$ and viscosity $\eta$, under gravity $g$, with a temperature difference $\Delta T$ between its base and its top, the Rayleigh number is

the ratio of the diffusion time $d^2/\kappa$ to the buoyant rise time $\eta/(\rho g\alpha\,\Delta Td)$.