Exploring the similarity relationships from the nondimensionalization of atmospheric turbulence

Abstract

Nondimensionalization, a theoretical approach for establishing interconnections among parameters within a set of equations, has proven to be an effective tool for the analysis of atmospheric turbulence. By applying nondimensionalization to turbulence equations, a concise form of dimensionless turbulence functions can be obtained. This process also yields several dimensionless parameters, defined as combinations of characteristic scales. From the dimensionless tensor \({B}\) and vector \({{\varvec{\beta}}}_{\theta}\) introduced in this study, the characteristic length scale, \({z}^{s}\), can be defined as an alternative of length scale in similarity theories. Using the data from observational station in Horqin Sandy Land, quantified verifications of similarity relationships are carried out. The dimensionless parameters derived from nondimensionalization is not only in accordance with traditional turbulence theories but also facilitate the derivation of relationships among other dimensionless parameters. This reveals new similarity relationships that supplement the Monin–Obukhov theory. Under conditions of flat terrain and steady motions, the new length scale gives rise to similarity relationships exhibiting “4/3” exponential and near-linear patterns, which are associated with turbulent transport. These results make it possible to obtain the turbulent fluxes directly from the statistics of meteorological elements, even in stable stratifications. Consequently, the method of nondimensionalization can be taken as a reference in parameterization schemes of turbulence and climate models, and is fruitful in prospect of further study on atmospheric turbulence.