A Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

Abstract

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.