Universal functions

From Glossary of Meteorology

universal functions

According to the Monin–Obukhov similarity theory, the dimensionless shear
temperature gradient
and other gradients in the surface layer are proportional to dimensionless universal stability functions, where M is wind speed, θ is potential temperature, u* is friction velocity, and θ* is the surface kinematic heat flux divided by friction velocity.

These functions have a value of nearly 1 for neutral stratification, range over 0 < (z/L) < 1 for unstable stratification, and z/L > 1 for stable stratification, where z is height above the surface and L is the Obukhov length. For strong stability (z/L >> 1) the universal functions are nearly constant. Presently the most-used universal functions are based on an experiment conducted in Kansas in 1968, with some corrections made in the succeeding 30 years. The accuracy is about 10% for unstable and 20% for stable stratification. The following empirical forms of the universal functions, based on a von Kármán constant of k = 0.4, are currently used. For unstable stratification:
For neutral stratification:
For stable stratification:
These universal functions are
also called flux-profile relationships.