## Abstract

A method of deriving new relationships between near-surface turbulent fluxes and vertical differences of wind speed and potential temperature between two levels in the atmospheric surface layer from simplified second-order turbulence closure models is presented. The paper aims at a coherent treatment of fair-weather conditions and the asymptotic free-convection limit. The traditionally used representation of wind and temperature profiles is modified to reflect the three-sublayer structure of the surface layer in accordance with recent proposals; this leads to a generalization of the profile method. The modification suggests a new framework for the analysis of empirical data gathered in statically unstable fair-weather conditions. A general formulation of the problem involves a set of integral equations, which is solved numerically; with this aim, a new “convective” vertical coordinate transformation suitable for the computation of the upper part of the profile is proposed. Two popular turbulence closure models are used to calculate flux–finite difference relationships in the atmospheric surface layer. Approximated forms of the resulting universal functions are proposed for practical applications, based on the results of numerical integration.

The main goals of the paper are to show the formalism of deriving the free-convection-safe surface flux calculation algorithms from turbulence closure models; to explore the implications for the convective boundary layer scaling and for the construction of surface layer algorithms, coming from the analysis of the model; and to provide additional criteria for evaluating and developing turbulence closure models, based on analysis of their properties at free convection.

The paper results in a new formulation of flux-profile relationships. The near-free-convection part of the profile is described in terms of heat flux, height, and the Monin–Obukhov parameter *ζ*; matches smoothly to the classic Monin–Obukhov solution; and transforms asymptotically, with vanishing shear, into a purely free convection regime.

A generalization of the method for application to a horizontally homogeneous, quasi-steady-state, shear-free, convective boundary layer, leads to results comparable to the predictions of the convection-induced stress regime theory despite the different approach taken here.

*Corresponding author address:* Dr. Lech Łobocki, Institute of Environmental Engineering Systems, Warsaw University of Technology, Nowowiejska 20, 00-653 Warsaw, Poland.