Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer

Abstract

Turbulent mixing lengths and the eddy Prandtl number are estimated by analyzing aircraft data from three different field programs and existing studies in the literature. For small scale turbulence, the estimated mixing lengths appear to decrease rapidly with increasing Richardson number (Ri) and then reach an approximately constant value of 2.5 m for Ri > 0.3 with large scatter. A least squares fit of the estimated mixing length for heat using the format of Louis et al. (1981) yields an asymptotic mixing length of 14.2 m for neutral stratification. This value represents the best fit to the turbulent fluxes for the observed cases of stratified flow rather than a direct calibration of turbulence in neutrally stratified flow for which there were no observations. Mixing length values estimated from stronger larger scale disturbances also show a decrease of mixing length with increasing Richardson number although the values of mixing lengths are categorically larger yielding an asymptotic value of 150 m. Apparently, the Richardson number by itself is not a good predictor for the strength of turbulent mixing although suitable alternatives for large scale models are not available. The Prandtl number increases with increasing Richardson number in agreement with previous studies but the scatter is large. The mixing length formulation is applied to a column model of the lower troposphere. The asymptotic mixing length and the stability-dependent Prandtl number are derived from the data analysis. For the very stable case, shear generation of turbulence in the upper part of the surface inversion layer can be more significant than surface based turbulence generation. Large scale subsidence may significantly reduce the depth of the overlying residual layer. Since the subsidence is difficult to estimate from observations, model comparisons with the observed data are not conclusive.