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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.