Monin–Obukhov length explained
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[1] in 1946.[2] [3] It is also known as the Monin–Obukhov length because of its important role in the similarity theory developed by Monin and Obukhov.[4] A simple definition of the Monin-Obukhov length is that height at which turbulence is generated more by buoyancy than by wind shear.
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. If not known, the virtual potential temperature flux can be apprioximated with:
[5] \overline{w'\theta
{w'\theta'}(1+0.61\overline{r})+0.61\overline{\theta} \overline{w'r'}
where
is potential temperature, and
is mixing ratio.
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
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).
Notes and References
- Book: Jacobson, Mark Z.. Fundamentals of Atmospheric Modeling. 10.1017/CBO9781139165389. 2. 2005. Cambridge University Press. 9780521839709.
- Obukhov . A.M.. 1946. Turbulence in an atmosphere with a non- uniform temperature.. Tr. Inst. Teor. Geofiz. Akad. Nauk. SSSR. 1. 95–115.
- Obukhov . A.M.. 1971. Turbulence in an atmosphere with a non-uniform temperature (English Translation). Boundary-Layer Meteorology. 2. 1 . 7–29. 1971BoLMe...2....7O . 10.1007/BF00718085 . 121123105 .
- Monin. A.S.. Obukhov . A.M.. 1954. Basic laws of turbulent mixing in the surface layer of the atmosphere.. Tr. Akad. Nauk SSSR Geofiz. Inst. 24. 163–187.
- Book: Stull, Roland B.. An introduction to boundary layer meteorology. 1. 1988. Kluwer Academic Publishers. 9027727686.