On the Turbulence Quantities in the Atmospheric Mixing Layer

Abstract

The turbulence quantities such as the RMS of the vertical speed δ_w, 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 h_m 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: δ_w=C_wW³*ξ1/4 δT=cTT*ξ-1/4 ε=Cε(W₃*/hm)ξ K_M=C_KMW*h_m 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 K_M, δ_w, δ_T, and ε, the vertical profiles of δw and δ_T are determined. The agreements of the above relations to the observations are fairly good.