Linear Approximations of the Second Turbulent Moments of the Atmospheric Convective Surface Layer in a Forced-Convection Sublayer

Abstract

The Monin–Obukhov similarity theory for the convective surface layer distinguishes two limiting cases: a dynamic limit and a free-convection limit. The dynamic limit for the convective surface layer is defined as a flow with a logarithmic profile of wind and a zero buoyancy flux at the underlying surface. The free-convection limit is characterized by a zero wind speed and a positive buoyancy flux at the underlying surface. The limits of the generalized Monin–Obukhov similarity theory are able to describe the higher order turbulent moments. In this paper, it is assumed that the convective surface layer consists of two sublayers: the lower dynamic sublayer adjacent to the surface and the upper forced-convection sublayer. The turbulent moments can be approximated separately for each sublayer. Linear approximations are suggested for the turbulent moments of the vertical velocity and the potential temperature variance in the forced-convection sublayer. The first-order expansion terms of them correspond to the free-convection limits of the Monin–Obukhov theory under no-wind conditions. The second-order expansion terms describe profiles of the turbulent moments in under convective conditions with a moderate wind. A comparison between the proposed approximations and experimental data strongly suggests that the linear approximation is correct within a forced-convection range.