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Monin-Obukhov Length

The Monin-Obukhov Length is the height above ground, where mechanically produced (by vertical shear) turbulence is in balance with the dissipative effect of negative buoyancy, thus where Richardson number equals to 1:

L = - \frac{u^3_*\bar\theta_v}{kg(\overline {w^'\theta^'_v})}

where u * is the frictional velocity, \bar\theta_v is the mean potential virtual temperature, \bar w^' is the perturbation scalar velocity' and θ * is a potential temperature scale (k). This can be further reduced using the similarity theory approximation:


to give:

L = \frac{u^2_*\bar\theta_v}{kg\theta_*}

The parameter θ * is proportional to \bar \theta_v (z_r) - \bar \theta_v (z_{0,h}) the vertical difference in potential virtual temperature. The greater \bar \theta_v at Z0,h in comparison with its value at Zr , the more negative the change in \bar \theta_v with increasing height, and the greater the instability in the of the surface layer. In such cases, L is negative with a small magnitude, since it is inversely proportional to u * . When L is negative with a small magnitude, \frac{z}{L} is negative with a large magnitude. Such values of \frac{z}{L} correspond to large instability due to buoyancy. Positive values of \frac{z}{L} correspond to increasing \bar \theta_v with altitude and stable stratification.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Monin-Obukhov_Length". A list of authors is available in Wikipedia.
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