Convective richardson number

From Glossary of Meteorology

convective Richardson number

A dimensionless number that contains factors similar to the bulk Richardson number, but where the velocities, temperatures, and depths are based on mixed-layer scaling parameters.

The convective Richardson number Ri* can be written as
where g is gravitational acceleration, ΔEZθv is the change of virtual potential temperature across the depth of the entrainment zone, zi is the depth of the mixed layer, θv is the average virtual potential temperature within the mixed layer, and w* is the Deardorff velocity. The depth of the entrainment zone, and the entrainment rate, are related to this convective Richardson number.

Nelson, E., R. Stull, and E. Eloranta 1989. A prognostic relationship for entrainment zone thickness. J. Appl. Meteor.. 28. 885–903.