Monin–Obukhov similarity theory
Monin–Obukhov (M–O) similarity theory describes the non-dimensionalized mean flow and mean temperature in the surface layer under non-neutral conditions as a function of the dimensionless height parameter, named after Russian scientists A. S. Monin and A. M. Obukhov. Similarity theory is an empirical method that describes universal relationships between non-dimensionalized variables of fluids based on the Buckingham π theorem. Similarity theory is extensively used in boundary layer meteorology since relations in turbulent processes are not always resolvable from first principles.
An idealized vertical profile of the mean flow for a neutral boundary layer is the logarithmic wind profile derived from Prandtl's mixing length theory, which states that the horizontal component of mean flow is proportional to the logarithm of height. M–O similarity theory further generalizes the mixing length theory in non-neutral conditions by using so-called "universal functions" of dimensionless height to characterize vertical distributions of mean flow and temperature. The Obukhov length (), a characteristic length scale of surface layer turbulence derived by Obukhov in 1946, is used for non-dimensional scaling of the actual height. M–O similarity theory marked a significant landmark of modern micrometeorology, providing a theoretical basis for micrometeorological experiments and measurement techniques.
