A Richardson number compares gravitational stratification with inertial or shear effects. Its precise form depends on the characteristic scales or local gradients being compared.
For a stratified parallel shear flow, the gradient Richardson number compares the squared buoyancy frequency with squared vertical shear. The Miles–Howard theorem excludes exponentially growing inviscid normal modes when this ratio is at least everywhere. Where , the equivalent criterion is written directly as .
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The Richardson number (\(Ri\)) is a dimensionless number used in fluid mechanics and meteorology to quantify the relative importance of buoyancy compared to mechanical stirring (or shear) in a flow. It is especially relevant in the study of stratified fluids, such as in atmospheric and oceanic flows.