SIMILARITY OF SCALARS UNDER STABLE CONDITIONS

The question whether two different scalars have the same behaviour in the surface layer under stable conditions is investigated. ''Similarit y'' of two scalars is defined in terms of the equality of their corres ponding dimensionless Monin-Obukhov similarity functions. Previous the oretical and experimental results concerning the issue are briefly rev iewed: they are found to be contradictory. An analytical derivation of the square of the correlation coefficient between two scalars is obta ined based on the correlation structure of the turbulent dissipation f unctions for stable conditions, when it can be assumed that the diverg ence of the vertical transport of scalar variance/covariance is neglig ible. The resulting expression elucidates some earlier conflicting res ults, 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 turb ulence data measured in nocturnal stable conditions during FIFE-89. Ou r results, both from the analytical derivation and the statistical ana lysis of turbulence data, confirm that under validity of the Monin-Obu khov similarity theory assumptions, the corresponding similarity funct ions 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.