# Obukhov length

From Glossary of Meteorology

## Obukhov length

A parameter with dimension of length that, when used to scale the height above the ground

*z*, yields a dimensionless stability parameter,*z*/*L*, that expresses the relative roles of shear and buoyancy in the production/consumption of turbulence kinetic energy.It is defined by where

The parameter was first described by Obukhov in 1946, and therefore should not be called the Monin–Obukhov length, even though there is a Monin–Obukhov similarity theory that uses it. The Obukhov length, typically of order one to tens of meters, is positive (negative) for stable (unstable) stratification and becomes infinite in the limit of neutral stratification (

*k*is von Kármán's constant,*u*_{*}is the friction velocity (a measure of surface stress),*Q*_{v0}is a kinematic virtual temperature flux at the surface,*T*_{v}is a reference virtual temperature, and*g*is the gravitational acceleration. The ratio*g*/*T*_{v}defines the buoyancy parameter, with*T*_{v}often taken to be the surface air temperature, consistent with the Boussinesq approximation.The parameter was first described by Obukhov in 1946, and therefore should not be called the Monin–Obukhov length, even though there is a Monin–Obukhov similarity theory that uses it. The Obukhov length, typically of order one to tens of meters, is positive (negative) for stable (unstable) stratification and becomes infinite in the limit of neutral stratification (

*Q*_{v0}= 0). The dimensionless Obukhov stability parameter*z*/*L*, which can be obtained directly from the flux Richardson number when approximating the wind speed gradient*du*/*dz*by*u*_{*}/*kz*, typically ranges from –5 to 5, with positive (negative) values indicating stable (unstable) values, and approaches 0 in the limit of neutral stratification.*Compare*similarity theory, dimensional analysis, Buckingham Pi theory, surface layer.Foken, T., 2006: 50 years of the Monin–Obukhov similarity theory. *Bound.-Layer Meteor.*, **119**, 431–447, doi:10.1007/s10546-006-9048-6.

*Term edited 20 July 2016.*