Dimensionless criteria for the production-dissipation equilibrium of scalar fluctuations and their implications for scalar similarity

In water resources it is common to consider that two scalars have a similar behavior in the atmospheric surface layer. This is a consequence of Monin-Obukhov similarity theory whose direct implication is that all similarity functions between two scalars are equal. However, many works show that scalar similarity does not always hold under unstable conditions, a fact for which it is often difficult to establish a physical cause. In this paper, using a data set measured during winter over a tropical lake in Brazil (Furnas Lake), we found a relation between temperature-water vapor similarity and the strength of the surface forcing; we also confirmed that the classical balance between gradient production and molecular dissipation of scalar variance and covariance is key to scalar similarity. This balance can be disrupted by large values of the third-order transport terms, and possibly by nonstationary terms as well. In connection with the scalar variance and covariance budgets, we propose a new set of dimensionless scalar flux numbers which are able to make a good diagnosis of the aforementioned balance (or the lack thereof) for each budget. The fact that different Monin-Obukhov functions are not equally capable of identifying scalar similarity is also demonstrated and a new bulk indicator of scalar flux similarity is proposed whose absolute value, unlike the relative transfer efficiency, is bounded above by 1; this new indicator holds also in the spectral domain. Finally, we verify that low-frequency dissimilarity has a larger impact over scalar similarity than over scalar flux similarity.