Similarity of scalars under stable conditions

Abstract

The question whether two different scalars have the same behaviour in the surface layer under stable conditions is investigated. “Similarity” of two scalars is defined in terms of the equality of their corresponding dimensionless Monin-Obukhov similarity functions. Previous theoretical and experimental results concerning the issue are briefly reviewed: they are found to be contradictory. An analytical derivation of the square of the correlation coefficient between two scalars is obtained based on the correlation structure of the turbulent dissipation functions for stable conditions, when it can be assumed that the divergence of the vertical transport of scalar variance/covariance is negligible. The resulting expression elucidates some earlier conflicting results, and helps to establish the equality of the similarity functions for all scalars in the stable surface layer. A statistical analysis in the time domain is also performed using temperature and humidity turbulence data measured in nocturnal stable conditions during FIFE-89. Our results, both from the analytical derivation and the statistical analysis of turbulence data, confirm that under validity of the Monin-Obukhov similarity theory assumptions, the corresponding similarity functions for temperature and humidity are equal to within the statistical uncertainty of the measurements. An important consequence is that the eddy diffusivities of temperature and humidity are also equal.