The local similarity theory, including the "spectral" Prandtl mixing length. Dissipation of energies and structural parameters in the atmospheric CBL

TL;DR

This paper introduces a variant of local similarity theory using spectral Prandtl mixing length, providing a unified framework to express turbulence parameters and confirming its accuracy with experimental data in atmospheric convective boundary layers.

Contribution

It develops a new local similarity approach incorporating spectral Prandtl mixing length, extending turbulence theories and improving understanding of atmospheric turbulent convection.

Findings

The theory accurately predicts turbulent exchange coefficients.

It aligns with established semi-empirical turbulence models.

The approach is validated against experimental data.

Abstract

The paper discusses a variant of the local similarity theory, employing the second moment of vertical velocity and the "spectral" Prandtl mixing length as basic parameters. This approach allows expressing the turbulent exchange coefficient, dissipations of kinetic energy and buoyancy square, mixed moments of the buoyancy and vertical velocity, as well as structural parameters solely through two independent basic parameters of local similarity. Comparison of local similarity approximations with experimental data convincingly confirms the correctness of the proposed relationships and demonstrates the high efficiency of the considered theory. It is established that the approximations of the turbulent exchange coefficient and dissipations of local similarity are fully consistent with the semi-empirical theories of Prandtl, Hanna, Richardson-Onsager and the Kolmogorov-Obukhov spectral theory with the law -5/3 for the atmospheric CBL. Thus, the new theory of local similarity significantly extends the scope of applications of well-known turbulence theories and substantially complements our understanding of turbulent convection.