We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO x –O3 triad problem. The chemical reactions involve one first-order reaction, the destruction of NO2 with decay time τ, and one second-order reaction, the destruction of NO and O3 with the reaction constant k. Since the fluxes of the sum concentrations of NO x = NO + NO2 and O3 + NO2 turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO2. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w * as the velocity unit, and the surface temperature flux divided by w * as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O3 and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.
- Wind energy
- Wind power meteorology