ESTIMATION OF THE MONIN-OBUKHOV SIMILARITY FUNCTIONS FROM A SPECTRAL MODEL MARTIN CLAUSSEN Max Planck Institut f?r Meteoroiogie, Bundesstra$e 55, 2000 Hamburg 13, F.R.G. (Received in final form 1 December, 1984)) Abstract. From measured one-~mension~ spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range - 2 2 z/L 2 + 2. The calculations show good agreement with observations with the exception of a range - 12 z/L 2 0 in which the function 4b,, ., i e the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy. Notation constants (see Equations (2-4)) constants i = u, v, W, B (see Equation (5)) peak wave numbers of 3-d model spectra of turbulent kinetic energy and of temperature variance, respectively peak wave numbers of l-d spectra of velocity components i = u, u, w and of temperature fluctuations i = 0 characteristic wave numbers of energy-feedingby mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively Monin-Obukhov length difference of mean temperature and mean potential temperature Monin-Obukhov temperature scale velocity of mean flow in positive x-direction friction velocity components of velocity fluctuations height above ground von Karman constant temperature fluctuation nondimension~ mean shear nondimensional mean temperature gradient nondimensional rate of molecular dissipation E of turbulent kinetic energy nondimensional divergence of vertical transports of turbulent kinetic energy 1. In~oduction Descriptions of turbulent boundary layers considering thermal stratification and stress by a mean shear have been based on similarity theories. A similarity theory of flows in the lower part of the atmospheric boundary layer was developedby Monin and Obukhov (1954). The universal functions of this similarity theory are used in many numerical models of atmosphe~c motions (e.g., Pielke, 198 1). The universal functions have been determined by experiments (e.g., Businger et a/., 1971; Dyer, 1974; Dyer and Bradley, 1982) and by empirical or semiemperical theories (e.g., Yamamoto, 1975). Boundary Layer Meteorology 33 (1985) 233-243. 0006-8314/85.15 0 1985 by D. Reidel Publishing Company.