Gradient richardson number

From Glossary of Meteorology

gradient Richardson number

A dimensionless ratio, Ri, related to the buoyant production or consumption of turbulence divided by the shear production of turbulence.

It is used to indicate dynamic stability and the formation of turbulence:
where θv is virtual potential temperature, Tv is virtual absolute temperature, z is height, g is gravitational acceleration, and (U, V) are the wind components toward the east and north. The critical Richardson number, Ric, is about 0.25 (although reported values have ranged from roughly 0.2 to 1.0), and flow is dynamically unstable and turbulent when Ri < Ric. Such turbulence happens either when the wind shear is great enough to overpower any stabilizing buoyant forces (numerator is positive), or when there is static instability (numerator is negative).
Compare bulk Richardson number, flux Richardson number, Froude number.