Local similarity theory including the “spectral” Prandtl mixing length and the second moment of vertical velocity: Comparison with semi-empirical turbulence theories in the atmospheric convective boundary layer

We discussed a variant of a new theory of local similarity (NTLS) that uses, as basic parameters, the “spectral” Prandtl mixing length and the second moment of the vertical velocity. This approach allows turbulent exchange coefficients, the dissipation of turbulent kinetic energy, and mixed moments of buoyancy and vertical velocity to be expressed solely through two independent basic parameters of local similarity. Comparison of the local similarity approximations with experimental data supports the proposed relations and demonstrates the high effectiveness of NTLS. The results of the new theory of local similarity are compared with well known semi-empirical turbulence theories. It is shown that, throughout the atmospheric convective boundary layer, the local similarity approximations for the turbulent exchange coefficient and the dissipation of kinetic energy are fully consistent with the relations of the semi-empirical theories of Prandtl, Richardson–Onsager, and Hanna. Under weak wind conditions, partial consistency with Taylor's semi-empirical theory is demonstrated. For the semi-empirical theories of von Kármán and Prandtl–Kolmogorov, partial consistency with local similarity is established. Above the surface convective layer, the relations of these theories differ from the NTLS approximations, while within the convective surface layer their relations are identical to the local similarity approximations. In the surface layer, the NTLS approximations are also compared with the classical Monin–Obukhov similarity theory (MOST). It is established that, in windless conditions, the surface asymptotics of NTLS are identical to the free convection limits of MOST.