Monin-Obukhov Length

The Obukhov length is used to describe the effects of buoyancy on turbulent flows, particularly in the lower tenth of the atmospheric boundary layer. It was first defined by Alexander Obukhov

Alexander Obukhov

Alexander Mikhailovich Obukhov was a Russian physicist and applied mathematician known for his contribution to statistical theory of turbulence and atmospheric physics. He was one of the founders of modern boundary layer meteorology...

 in 1946, . It is also known as the Monin-Obukhov length because of its important role in the similarity theory developed by Monin and Obukhov .

The Obukhov Length is defined by


where is the frictional velocity, is the mean virtual potential temperature, is the surface virtual potential temperature flux, k is the von Kármán constant

Von Kármán constant

In fluid dynamics, the Von Kármán constant , named for Theodore von Kármán, is a dimensionless constant describing the logarithmic velocity profile of a turbulent fluid flow near a boundary with a no-slip condition...

. The virtual potential temperature flux is given by


where is potential temperature, is absolute temperature and is specific humidity.

By this definition, is usually negative in the daytime since is typically positive during the daytime over land, positive at night when is typically negative, and becomes infinite at dawn and dusk when passes through zero.

A physical interpretation of is given by the Monin-Obukhov similarity theory. During the day it is the height at which the buoyant production of turbulence kinetic energy (TKE) is equal to that produced by the shearing action of the wind (shear production of TKE).