View source for 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]]<ref>{{cite book|last=Jacobson|first=Mark Z.|title=Fundamentals of Atmospheric Modeling|doi=10.1017/CBO9781139165389|edition=2|year=2005|publisher=[[Cambridge University Press]]|isbn=9780521839709}}</ref> in 1946.<ref>{{cite journal |last1=Obukhov |first1=A.M.|year=1946|title=Turbulence in an atmosphere with a non- uniform temperature.|journal= Tr. Inst. Teor. Geofiz. Akad. Nauk. SSSR|volume=1|pages=95–115}}</ref><ref>{{cite journal |last1=Obukhov |first1=A.M.|year=1971|title=Turbulence in an atmosphere with a non-uniform temperature (English Translation)| journal=Boundary-Layer Meteorology|volume=2|issue=1 | pages=7–29|bibcode = 1971BoLMe...2....7O |doi = 10.1007/BF00718085 |s2cid=121123105 }}</ref> It is also known as the Monin–Obukhov length because of its important role in the similarity theory developed by [[Andrei Monin|Monin]] and Obukhov.<ref>{{cite journal |last1=Monin|first1=A.S.|last2=Obukhov |first2=A.M.|year=1954|title=Basic laws of turbulent mixing in the surface layer of the atmosphere.|journal= Tr. Akad. Nauk SSSR Geofiz. Inst|volume=24|pages=163–187}}</ref> 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

:<math>
L = - \frac{u^3_*\bar\theta_v}{kg(\overline {w^'\theta^'_v})_s}\ 
</math>

where <math>u_*</math> is the [[Friction velocity|frictional velocity]], <math>\bar\theta_v</math> is the mean virtual [[potential temperature]], <math>(\overline{w^'\theta^'_v})_s</math> 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:<ref>{{cite book|last=Stull|first=Roland B.|title=An introduction to boundary layer meteorology|edition=1|year=1988|publisher=[[Kluwer Academic Publishers]]|isbn=9027727686}}</ref>

:<math>
\overline {w^'\theta^'_v}=\overline {w^'\theta^'}(1+0.61\overline{r})+0.61\overline{\theta}\; \overline {w^'r^'}
</math>

where <math>\theta</math> is potential temperature, and <math>r</math> is mixing ratio. 


By this definition, <math>L</math> is usually negative in the daytime since <math>\overline {w^'\theta^'_v}</math> is typically positive during the daytime over land, positive at night when <math>\overline {w^'\theta^'_v}</math> is typically negative, and becomes infinite at dawn and dusk when <math>\overline {w^'\theta^'_v}</math> passes through zero.

A physical interpretation of <math>L</math> is given by the [[Monin–Obukhov similarity theory]]. During the day <math>-L</math> 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).

==References==
{{Reflist}}

{{DEFAULTSORT:Monin-Obukhov length}}
[[Category:Atmospheric dispersion modeling]]
[[Category:Boundary layer meteorology]]
[[Category:Fluid dynamics]]
[[Category:Buoyancy]]
[[Category:Meteorology in the Soviet Union]]
[[Category:Microscale meteorology]]

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