  In a reaction-diffusion-advection system, with a convectively unstable
regime, a perturbation creates a wave train that is advected downstream and
eventually leaves the system. We show that the convective instability coexists
with a local absolute instability when a fixed boundary condition upstream is
imposed. This boundary induced instability acts as a continuous wave source,
creating a local periodic excitation near the boundary, which initiates waves
traveling both up and downstream. To confirm this, we performed analytical
analysis and numerical simulations of a modified Martiel-Goldbeter
reaction-diffusion model with the addition of an advection term. We provide a
quantitative description of the wave packet appearing in the convectively
unstable regime, which we found to be in excellent agreement with the numerical
simulations. We characterize this new instability and show that in the limit of
high advection speed, it is suppressed. This type of instability can be
expected for reaction-diffusion systems that present both a convective
instability and an excitable regime. In particular, it can be relevant to
understand the signaling mechanism of the social amoeba Dictyostelium
discoideum that may experience fluid flows in its natural habitat.
