Flux richardson number

From Glossary of Meteorology

flux Richardson number

A dimensionless number defined as the ratio of the buoyancy term of the turbulence kinetic energy budget equation and the negative of the shear terms of that same equation:

where g is gravitational acceleration, z is height, θv is virtual potential temperature, Tv is the virtual temperature, (U, V) are the horizontal Cartesian wind components from the west and the south, primes denote deviations from mean values, and overbars denote the mean or average. It is a measure of dynamic stability, which describes the capability of the flow to remain turbulent by wind shear overpowering any static stability. Normally, the denominator is negative. Thus, when the numerator is positive, the flux Richardson number Rf is negative for statically unstable air. When the flux Richardson number is less than 1, the flow is dynamically unstable and is turbulent. When the flux Richardson number becomes greater than 1, the flow becomes dynamically stable, turbulence would tend to decay, and the flux Richardson number would become undefined.
Compare gradient Richardson number, bulk Richardson number, critical Richardson number.