To determine if the flow regime is laminar or turbulent, in general we calculate the Reynolds number. This is the Reynolds number which defines the nature of the flow regime.
The Rayleigh number (Ra) is a dimensionless number used in fluid mechanics and heat transfer characteristic within a fluid: less than a critical value of about 2000, the transfer operates primarily by conduction, while that beyond this value it is the free or natural convection becomes important.
The critical value of Rayleigh number characterizing the laminar-turbulent transition in natural convection depends on the fluid thermophysical properties, the geometry of the physical domain and the surface roughness (similarly to the critical Reynolds number in forced flows). As far as I know there is no well-established value for critical Rayleigh number, but it is reported that turbulence occurs in natural convection at Ra>10^6 in an enclosed cavity, at Ra>10^7 over a horizontal flat-plate, and at Ra>10^9 over a vertical flat-plate.