# Universal functions

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## 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 < (For neutral stratification: For stable stratification: These universal functions are

*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:*also called*flux-profile relationships.