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 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. 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 ${\displaystyle u_{*}}$ is the frictional velocity, ${\displaystyle {\bar {\theta }}_{v}}$ is the mean virtual potential temperature, ${\displaystyle ({\overline {w^{'}\theta _{v}^{'}}})_{s}}$ is the surface virtual potential temperature flux, k is the von Kármán constant. The virtual potential temperature flux is given by

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