A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer |
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| Authors: | Leif Kristensen Donald H Lenschow David Gurarie Niels Otto Jensen |
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| Institution: | 1.Ris? DTU National Laboratory for Sustainable Energy,Roskilde,Denmark;2.National Center for Atmospheric Research,Boulder,USA;3.Department of Mathematics,Case Western Reserve University,Cleveland,USA |
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| Abstract: | 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. |
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