  Algebraic closure models with spatially nonlocal operators that are
associated with both unresolved advective transport and nonlinear reaction
terms in a Reynolds-averaged Navier-Stokes context are presented in this work.
In particular, a system of two species subject to binary reaction and transport
by advection and diffusion are examined by expanding upon analysis originally
developed for binary reactions in the context of Taylor dispersion of scalars.
This work extends model forms from weakly-nonlinear extensions of that
dispersion theory and the role of nonlocality in the presence of reactions is
studied and captured by analytic expressions. These expressions can be
incorporated into an eddy diffusivity matrix that explicitly capture the
influence of chemical kinetics and flow conditions on the closure operators and
we demonstrate that the model form derived in a laminar context can be directly
translated to an analogous setup in homogeneous isotropic turbulence, which has
implications as a subgrid scale model. We show that this framework can improve
prediction of mean quantities compared to previous purely local results, but
does not fully close unresolved terms.
