| Summary: | The von Karmãn constant (k) and the Monin-Obukhov similarity formulation occupy very important positions in the theoretical framework of the atmospheric surface layer (ASL). Measurements, however, provide a great scatter in their estimates mainly because the requirements of neutrality (only for estimate of tc), stationarity and horizontal homogeneity in the real atmospheric boundary layer (ABL) are hardly achieved. Therefore, a long-time dispute over the value of the von Karman constant applicable in the neutral-static-stability ABL has not been settled yet; another controversy concerns the form of the universal Monin-Obukhov similarity functions in very unstable conditions.
A numerical tool, three-dimensional large eddy simulation (LES), is adopted to simulate turbulence in the ABL, with a fine resolution in the ASL, so that an "a priori value” of the von }Carman constant and the Monin-Obukhov similarity formulas can be derived from the resolved-scale turbulence in the upper surface layer (USL). Only an ideal geometry, flat but rough surface, is treated. Horizontal homogeneity of all dependent mean variables is assumed except the mean pressure, which is the driving mechanism of the whole turbulent boundary layer due to the geostrophic flow aloft. Smagorinsky's sub grid scale (SGS) model is adopted. In the present study, the Smagorinsky-model Reynolds number (Resm) is proposed for a LES adopting the Smagorinsky SGS model. This number is shown to be an independent model parameter, which determines the statistics of resolved scale (RS) turbulence in the USL. If Resm is smaller than a critical value, RS fields are damped out. This fact establishes a criterion for a LES adopting the Smagorinsky SGS model. For a neutral-static-stability ABL, the present study uses grid spacings that fall within the inertial sub range of the USL turbulence in order to follow the assumption of the Smagorinsky SGS model. Other specifications of grid spacing are also used to show the influence of grid spacing and validity of &sm. The largest computation involves 64 x 64 x 50 grids. The average of the velocity fields over the whole horizontal plane and time domain yields a logarithmic velocity profile in the USL, from which the von Kãrman constant can be derived. The value of IC found in the study ranges from 0.17 to 0.35, depending on the value of Resm when the domain size and the Ross by number are fixed. Other quantities in the USL, such as profiles of (l2)/u, (432)/n2, (ti.52)/n2, _(ti))/n*2 and—(i)/u, also exhibit a very strong dependence on Resm. For an unstable ABL, in which an additional turbulent sensible heat flux is imposed on the surface, profiles of the mean velocity in the USL yield a Monin-Obukhov similarity formula for the dimensionless momentum flux. For —5 < zIL < —1, where L is the Monin-Obukhov length, the formula gives smaller values of 077,(z/L) than existing empirical formulas, but close to Carl et al.'s —1/3 power law (1973). LES results of o-o/T*,, fit the empirical similarity formulas fairly well, and derive a power law exponent of about —0.4, which is smaller than —1/3. Similarity results for uti-,/u* in the USL has also been examined.
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