Spatial organization in the A+B→0 reaction under confined-scale mixing

We consider the kinetics of the two-dimensional, stoichiometric $\text{A+B→0}$ reaction under confined-scale turbulent mixing and concentrate on the interplay between the kinetic patterns and the spatial organization of the system. We study the properties of the arising clusters and of the reaction zones, both in the presence and in the absence of mixing. We show that the two- point correlation function $C_{\mathrm{AB}}{\mathrm{(r)=〈c}}_A({r}\mathrm{\prime +}{r}{\mathrm{)c}}_B({r}{\mathrm{\prime )〉/〈c}}_A({r}{\mathrm{)〉}}^2$ is closely related to the effective reaction rate, while the functional form of the quartic correlation function ${\mathrm{Q(r,t)=〈c}}_A({r}{\mathrm{\prime ,t)c}}_B({r}{\mathrm{\prime ,t)c}}_A({r}\mathrm{\prime +}{r}{\mathrm{,t)c}}_B({r}\mathrm{\prime +}{r}{\mathrm{,t)〉/〈c}}_A^2({r}{\mathrm{,t)c}}_B^2({r}\mathrm{,t)〉}$ is connected to the geometry of the reaction zones. We pay special attention to the occurrence of time windows of fast (classical) concentration decay even when the reactants show strong segregation.