Local similarity theory of convective turbulent layer using ‘spectral’ Prandtl mixing length and second moment of vertical velocity

Approximations of the turbulent moments of the atmospheric convective boundary layer are constructed based on a variant of the local similarity theory. As the basic parameters of this theory, the second moment of vertical velocity and the ‘spectral’ Prandtl mixing length are used. This specific choice of the basic parameters allows us to consider the coefficient of turbulent transfer and the dissipation of kinetic energy of the Prandtl turbulence theory as the forms of the local similarity. Therefore, the obtained approximations of the turbulent moments should be considered as natural complementation to the semi-empirical turbulence theory. Moreover, within the atmospheric surface layer, the approximations of the new local similarity theory are identical to the relations of the Monin-Obukhov similarity theory (MOST). Therefore, the proposed approximations should be considered as a direct generalization of the MOST under free convection conditions. The new approximations are compared with the relations of the known local similarity theories. The advantages and limitations of the new theory are discussed. The comparison of the approximations of the new local similarity theory with the field and laboratory experimental data indicates the high effectiveness of the proposed approach.