A Relationship of the Reynolds Stress to Local Shear and Heat Fluxes in the Planetary Boundary Layer

Abstract

The steady Reynolds stress and turbulent energy equations for steady, horizontally homogeneous mean flow are used to relate the Reynolds stress u?w? to the mean wind shear and heat fluxes in the planetary boundary layer. The resulting Reynolds stress demonstrates a 3/2 power dependence on the stress Richardson number and a ½ power dependence on the flux Richardson number. Numerical results of Deardorff are used to estimate vertical profiles of a heat flux function which results from the derivation. Such calculations and certain observations suggest that the stress depends mainly on the flux Richardson number in the upper part of the strongly heated boundary layer but more on the stress Richardson number in the lower part of the weakly heated or stable boundary layer. The simple model developed appears to be inadequate in the case of large?z/L where the shear generation of stress becomes negligible and turbulent transports of stress may be significant.