Two-species reaction–diffusion system in the presence of random velocity fluctuations

We study random velocity effects on a two-species reaction–diffusion system consisting of three reaction processes $A+A\to(\varnothing,A)$, $A+B\to A$. Using the field theory perturbative renormalization group, we analyze this system in the vicinity of its upper critical dimension $d_{\mathrm c}=2$. A velocity ensemble is generated by means of stochastic Navier–Stokes equations. In particular, we investigate the effect of thermal fluctuations on the reaction kinetics. The overall analysis is performed in the one-loop approximation and possible macroscopic regimes are identified.