On the Turbulence Quantities in the Atmospheric Mixing Layer

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Abstract
The turbulence quantities such as the RMS of the vertical speed δw, and temperature δT, the dissipation rate of kinetic energy to heat ε, and the vertical diffusion coefficient KM, in the free convective mixing layer have been considered. Taking velocity scale W* and temperature scale T* for the convection layer, which has been proposed by Deardorff (1970) and others, and the depth of the mixing layer hm as scale height, the relations describing these quantities in the free convective constant flux layer are extended to the free convective mixing layer. These turbulence quantities are written as follows: δw=CwW3*ξ1/4 δT=cTT*ξ-1/4 ε=Cε(W3*/hm)ξ KM=CKMW*hm where C is a universal constant, ξ=1-z/hm, and z is height. The vertical profile of ε is determined by using the energy balance equation for the and temperature scale T* for the free convection layer, which has been proposed by Deardorff free convective layer and assuming linearly decreasing vertical heat flux with height as shown by many observations. Also, according to observed results, KM is assumed to be invariant with height. Moreover, using dimensional relations among KM, δw, δT, and ε, the vertical profiles of δw and δT are determined. The agreements of the above relations to the observations are fairly good.