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Publikacja

Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory

Yano J.-I., Waclawczyk M.

Boundary-Layer Meteorology

182, 2022, 417-439, 10.1007/s10546-021-00657-7

The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.


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