The Rayleigh number compares buoyancy driving with viscous and thermal diffusion. For a layer of thickness , temperature drop , density , thermal expansion coefficient , gravitational acceleration , thermal diffusivity , and dynamic viscosity ,Thermal convection begins when this exceeds a geometry-dependent critical value.
A local Rayleigh-number closure estimates the thickness of a turbulent thermal boundary layer by settingwhere is an order-one or geometry-dependent critical value. Combining this with Fourier's law converts the boundary-layer temperature and density differences into a heat flux law.
Penetrative convection occurs when an unstable convecting region extends into, or is capped by, a stably stratified region. Water near its temperature of maximum density provides a common example: a cold stable layer can lie above a warmer turbulent convecting layer.
Fresh water reaches maximum mass density near at atmospheric pressure. A useful local equation of state isso water becomes less dense when its temperature moves either above or below .
In an ice-covered freshwater lake, a stagnant layer colder than the density-maximum temperature can cap a warmer turbulent region. Maximizing the boundary-layer heat flux obtained from a Local Rayleigh-number closure gives an interface temperature satisfyingand a maximum upward heat flux proportional to .
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The Rayleigh number (Ra) is a dimensionless number that characterizes the flow and stability of fluids in a system when buoyancy forces are significant compared to viscous forces. It is particularly important in the study of convection, particularly natural convection, where fluid motion is induced by differences in temperature and thus density.