Editing Rayleigh number (section)

===Geophysical applications===
In [[geophysics]], the Rayleigh number is of fundamental importance: it indicates the presence and strength of convection within a fluid body such as the [[Earth's mantle]]. The mantle is a solid that behaves as a fluid over geological time scales. The Rayleigh number for the Earth's mantle due to internal heating alone, Ra''<sub>H</sub>'', is given by:

<math display="block">\mathrm{Ra}_H = \frac{g\rho^{2}_{0}\beta HD^5}{\eta \alpha k}</math>

where:
*''H'' is the rate of [[radiogenic heat]] production per unit mass
*''η'' is the [[dynamic viscosity]]
*''k'' is the [[thermal conductivity]]
*''D'' is the depth of the [[Mantle (geology)|mantle]].<ref name=Bunge>{{cite journal |first1=Hans-Peter |last1=Bunge |last2=Richards |first2=Mark A. |last3=Baumgardner |first3=John R. |year=1997 |title=A sensitivity study of three-dimensional spherical mantle convection at 10<sup>8</sup> Rayleigh number: Effects of depth-dependent viscosity, heating mode, and endothermic phase change| journal = [[Journal of Geophysical Research]] | pages = 11991–12007 | volume = 102 |issue=B6 |doi=10.1029/96JB03806 |bibcode = 1997JGR...10211991B |doi-access=free }}</ref>

A Rayleigh number for bottom heating of the mantle from the core, Ra''<sub>T</sub>'', can also be defined as:

<math display="block">\mathrm{Ra}_T = \frac{\rho_{0}^2 g\beta\Delta T_\text{sa}D^3 C_P}{\eta k}</math>

where:
*Δ''T''<sub>sa</sub> is the superadiabatic temperature difference (the superadiabatic temperature difference is the actual temperature difference minus the temperature difference in a fluid whose [[entropy]] gradient is zero, but has the same profile of the other variables appearing in the [[equation of state]]) between the reference mantle temperature and the [[core–mantle boundary]]
*''C<sub>P</sub>'' is the [[specific heat capacity]] at constant pressure.<ref name=Bunge />

High values for the Earth's mantle indicates that convection within the Earth is vigorous and time-varying, and that convection is responsible for almost all the heat transported from the deep interior to the surface.