Richardson number

The Richardson number is named after Lewis Fry Richardson (1881 - 1953). It is the dimensionless number that expresses the ratio of potential to kinetic energy (modellers will be more familiar with the reciprocal of the square root of the Richardson number, known as the Froude number).

where g is the acceleration due to gravity, h a representative vertical lengthscale, and u a representative speed.

When considering flows in which density differences are small (the Boussinesq approximation), it is common to use the reduced gravity g' and the relevant parameter is the densimetric Richardson number

which is used frequently when considering atmospheric or oceanic flows.

If the Richardson number is much less than unity, buoyancy is unimportant in the flow. If it is much greater than unity, buoyancy is dominant (in the sense that there is insufficient kinetic energy to homogenize the fluids).

If the Richardson number is of order unity, then the flow is likely to be buoyancy-driven: the energy of the flow derives from the potential energy in the system originally.