Richardson number

The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term:

where ${\displaystyle g}$ is gravity, ${\displaystyle \rho }$ is density, and ${\displaystyle u}$ is a representative flow speed.

The Richardson number, or one of several variants, is of practical importance in weather forecasting and in investigating density and turbidity currents in oceans, lakes, and reservoirs.

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

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