From AMS Glossary
The nondimensional ratio between the product of buoyancy forces and heat advection and the product of viscous forces and heat conduction in a fluid.
It is written as
where g is the acceleration of gravity, ΔzT a characteristic vertical temperature difference in the characteristic depth d, α the coefficient of expansion, ν the kinematic viscosity, and k the molecular conductivity. The Rayleigh number is equal to the product of the Grashoff and Prandtl numbers, and is the critical parameter in the theory of thermal instability for laboratory flows.