The Rayleigh number is a dimensionless quantity that measures the ratio of buoyancy-driven convective forces to viscous and thermal diffusive damping forces in a fluid layer heated from below; convection begins (the onset of convection) only once the Rayleigh number exceeds a critical threshold value, which for idealized fluid layers is on the order of about 1000 (more precisely around 1708 for rigid boundary conditions, or about 657 for free boundaries), below which conductive heat transfer dominates and no convective overturn occurs.
The Rayleigh number Ra = (g alpha delta-T d^3)/(kappa nu), combining gravitational acceleration, thermal expansion coefficient, the temperature difference across the layer, the layer thickness,...
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