We consider the binary diffusion-controlled reaction A+B-->0 between nonpassively advected particles. This reactive system under a two-dimensional synthetic stationary turbulent flow leads to a diversity of kinetic regimes that result from the interplay between reaction, advection, and drag forces. Inertial bias collects particles preferentially in certain regions of the flow depending on their density, and this fact strongly determines the overall kinetic behavior and the spatial organization of the reactive mixture. A Eulerian scheme for the equations that describe this problem is developed and implemented, so that we can numerically follow the decay behavior as well as the patterned evolution of the system. Two-point correlation functions are used in order to characterize the aggregation versus segregation phenomena taking place in the system.