Experiments and stochastic simulations are presented as evidence for the convective nature of the differential flow instability, observed in a tubular flow reactor, using the Belousov-Zhabotinsky system as the active medium. The irregular spacing and amplitudes of the traveling wave fronts is characteristic of the noise-induced structures that arise through the convective instability. When recycling of the reactive flow is introduced in the simulations in the form of periodic boundary conditions, the waves become periodic and the instability absolute. The average concentrations of both activator and inhibitor are enhanced in the patterned state, and the enhancements are greater under conditions of absolute than under convective instability.