Wind and Temperature Profiles for Constant-flux Boundary Layers in Lapse Conditions with a Variable Eddy Conductivity to Eddy Viscosity Ratio

Abstract

A set of wind and temperature profile formulas are derived for the constant-flux atmospheric boundary layer in lapse stratification. These formulas imply a relationship between the eddy transfer coefficient ratio, KH/KM, and the stability parameter, s/L, as well as relationships between various empirical constants appearing in previously suggested profile forms. The derivation follows from the hypothesis that the gradient Richardson number, Ri, is equal to the Monin-Obukhov number, z/L. Empirical evidence is presented which supports the hypothesis when observational uncertainties in measured vertical wind and temperature differences are taken into account. The relationships between the empirical constants are consistent with previously reported values of these constants. The newly-derived free-convection wind profile agrees well with observed profiles reported by Swinbank (1964). The derived free-convection wind profile is found to be noticeably, if slightly, more consistent with observed wind profiles than is either Taylor's (1960) free-convection wind profile or Swinbank's (1964) exponential wind profile. The observed ratio of wind gradients for different layers is apparently constant with L in free-convection conditions. This is found to be consistent with the newly derived profile law and inconsistent with the KEYPS function profile law with constant KH/KM (Panofsky, 1963). However, the variation of the KEYPS function profile ratio lies within the observational uncertainty. It is concluded that the assumptions listed above provide a realistic description of the constant-flux surface boundary layer in lapse conditions within the accuracy of reported observations. The probable validity of the formulas for the eddy coefficient ratio is inferred from these results. Some practical aspects of the use of the profile laws are discussed.