Local Free Convection, Similarity, and the Budgets of Shear Stress and Heat Flux

Abstract

Equations for the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived. The behavior of the production and turbulent transport (flux divergence) terms in each budget is determined directly from measurements obtained over a wide range of stability conditions during the 1968 Kansas field program of AFCRL. The data are presented in the dimensionless form suggested by Monin-Obukhoy similarity theory, and follow universal functions quite well. The theory is extended to the ?local free convection? regime which exists under very unstable conditions, and specific power law forms are predicted. Several of these are verified and values are given for the proportionality factors in the power laws. The flux divergence terms are small, implying that in each budget the local production and destruction rates are in balance. The third moments which represent the vertical fluxes of stress and heat flux are small under stable conditions, but are large on the unstable side and indicate that turbulence transfers shear stress and heat flux upward at a velocity u*.