Realistic numerical experiments on the turbulent transport and mixing of reactants require the use of large-eddy simulation (LES). In the atmospheric boundary layer, the scales associated with turbulent motions range from the Kolmogorov dissipation scale (on the order of a millimeter) to the boundary layer depth (on the order of a kilometer). The largest eddies are responsible for the turbulent transport of the scalars and momentum whereas the smallest ones are mainly dissipative. LES consists of explicitly resolving all scales larger than the grid scale (on the order of tens of meters in the ABL), while the smallest (less energetic) scales are parameterized using a subgrid-scale (SGS) model.

An important challenge in large-eddy simulations of the atmospheric boundary layer is the specification of the SGS model coefficients and, in particular, how to account for external or internal parameters such as position in the flow, grid/filter scale, atmospheric stability and chemical regime. In large-eddy simulation, the filtered conservation equation for a reacting scalar involved in a second-order reaction

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is

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The effect of the unresolved scales on the evolution of the filtered scalar concentration appears through the subgrid-scale (SGS) flux, defined as

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and in the SGS reactant covariance that accounts for the mixing of the reactant at subgrid scales. This latter SGS quantity appears in the total covariance as

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Usually in LES of atmospheric turbulent reacting flows, the subgrid reactant flux is modeled as the product of a local gradient of the concentrations from the resolved scales and eddy-diffusivity coefficients and the subgrid reactant covariance is neglected.

References:

  • Vinuesa J.-F. , and F. Porté-Agel, 2005: A dynamic similarity subgrid model for chemical transformations in large eddy simulation of the atmospheric boundary layer. Geophysical Research Letters, 32, L03814.
  • Vinuesa J.-F. , F. Porté-Agel, S. Basu, and R. Stoll, 2006: Subgrid-scale modeling of reacting scalar fluxes in large-eddy simulations of atmospheric boundary layers. Environmental Fluid Mechanics, 6, 115-131.
  • Vinuesa J.-F. , and F. Porté-Agel, 2008: Dynamic models for the subgrid scale mixing of reactants in atmospheric turbulent reacting flows. Journal of the Atmospheric Sciences, 65, 1692–1699.