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Zbigniew Sorbjan

Abstract

The parameterization of the mixed layer based on a decomposition of statistical moments into nonpenetrative and residual components and on their local similarity is discussed. The method is examined by using laboratory data for nonpenetrative convection and large-eddy simulation (LES) results for penetration convention. The examination allows discussion of various scales and similarity functions in the convective atmospheric boundary layer. Local similarity is demonstrated to be equivalent to a Level-2 closure scheme of Mellor and Yamada. The derived similarity functions are shown to agree with experimental data and with the results of numerical simulation.

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Zbigniew Sorbjan

Abstract

A simple, steady-state, numerical model is used to examine the Rossby-number similarity theory of the atmospheric boundary layer over a slightly inclined terrain. The model confirms the similarity predictions. The slope-influenced universal profiles of the wind velocity defects and the stress components are obtained by the model simulation.

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Zbigniew Sorbjan

Abstract

Effects caused by variation of the potential temperature lapse rate Γ in the free atmosphere are examined based on a “large eddy simulation” model of the shear-free convective atmospheric boundary layer. The obtained results show that only near the top of the boundary layer are the statistical moments involving temperature strongly sensitive to changes of the parameter Γ. Furthermore, the moments involving only the vertical velocity are practically independent of Γ. The ratio R of the heat fluxes at the top and the bottom of the mixed layer increases when Γ increases. For the values of Γ from 1 to 10 K/km, typically observed in the atmosphere, the heat flux ratio R varies in the range −0.2 to −0.3. When Γ increases by an order of magnitude to 100 K/km, R increases only slightly to about −0.4. When Γ decreases to zero, the heat flux Hi, at the top of the mixed layer also decreases to zero. In this case, the thermal structure of the atmospheric boundary layer is found to be similar to nonpenetrative “solid lid” convection in a tank.

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Zbigniew Sorbjan

Abstract

Monin-Obukhov similarity applied to the real part of the refractive index variance n2 is discussed. It is shown that, because the observed correlation coefficient rTQ between temperature and humidity is less than unity, scaling by n * = nw/u * (where u * is the friction velocity) makes the dimensionless variance n2/n*2 dependent on two dimensionless parameters, on dimensionless height z/L (where L is the Monin-Obukhov length), and on a parameter R, which is related to the Bowen ratio. As the Monin-Obukhov similarity framework is applied, a large scatter of the dimensionless refractive index variance is expected for certain values of the Bowen ratio. Such a scatter can be eliminated if a new scale N *, defined as a combination of temperature and humidity scales, is employed.

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Zbigniew Sorbjan

Abstract

A large eddy simulation model was used to generate and compare statistics of turbulence during nonpenetrative and penetrative dry convection. In penetrative convection dimensionless vertical velocities in updrafts were found to have almost the same values as in the nonpenetrative case. The countergradient transport of heat and moisture was found to be present during nonpenetrative convection at z/z i > 0.6. For penetrative convection the countergradient transport of heat occurred only in a layer 0.5 < z/z i < 0.75, while the countergradient transport of humidity was not present. During nonpenetrative convection, temperature and humidity were perfectly correlated. In penetrative convection the correlation coefficient was found to be less than unity, varying from about 0.9 near the surface to about −0.7 at the top of the mixed layer.

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Zbigniew Sorbjan

Abstract

A parameterization method developed by Sorbjan is used to derive expressions for various statistical moments of vertical velocity, potential temperature, and humidity (or passive scalar concentration) in the convective boundary layer. The method is based on decomposing statistical moments into nonpenetrative and residual components, and their local (height-dependent) scaling. The resulting expressions are compared with atmospheric and laboratory data, and also with the results of large-eddy simulation models. An agreement between the similarity functions and the experimental data is obtained.

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Zbigniew Sorbjan

Abstract

The structure of the steady-state flow, homogeneous along an inclined, flat, underlying surface, is studied. On the basis or the atmospheric boundary layer equations the resistance laws of geostrophic drag and heat transfer are obtained. The general form of the resistance law universal functions is found. The slope influence is shown in the figures, which were obtained by numerical solution of the resistance laws.

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Zbigniew Sorbjan

Abstract

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Zbigniew Sorbjan

Abstract

The paper investigates similarity of scalar fields in a horizontally homogeneous, cloud-free, shearless, convective mixed layer. The concept of the “bottom-up” and “top-down” decomposition is verified for both passive and active scalars, based on a number of large eddy simulations. The bottom-up diffusion is not confirmed to be countergradient. The top-down scaling, based on the values of entrainment fluxes, is found to be inefficient. Alternative sets of scales are proposed and validated for mean values of scalars. For the bottom-up process, the“free-convective” scaling is applied. For the top-down processes, new scales are based on the maximum values of scalar gradients in the interfacial layer. The bottom-up and top-down similarity functions for passive and active scalars are found equal.

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Zbigniew Sorbjan

Abstract

The similarity theory of an atmospheric boundary layer over a slightly inclined terrain, discussed in an earlier paper (Sorbjan, 1983) is extended to the case of geostrophic wind varying with height. The forms of resistance laws and universal functions are obtained in the cases when the Ekman height or the actual boundary layer height are used as the boundary layer height scales.

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