Monin-Obukhov Length

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_*ar heta_v}{kg(overline {w^' heta^'_v})}

where u_* is the frictional velocity, ar heta_v is the mean potential virtual temperature, ar w^' is the perturbation scalar velocity' and heta_* is a potential temperature scale (k). This can be further reduced using the similarity theory approximation:

(overline{w^' heta^'_v})_sapprox-u_* heta_*

to give:

L = frac{u^2_*ar heta_v}{kg heta_*}

The parameter heta_* is proportional to ar heta_v (z_r) - ar heta_v (z_{0,h}) the vertical difference in potential virtual temperature. The greater ar heta_v at Z_{0,h} in comparison with its value at Z_r , the more negative the change in ar heta_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 heta_*. 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 ar heta_v with altitude and stable stratification.


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