  Reactive Rayleigh-Taylor systems are characterized by the competition between
the growth of the instability and the rate of reaction between cold (heavy) and
hot (light) phases. We present results from state-of-the-art numerical
simulations performed at high resolution in 2d by means of a self-consistent
lattice Boltzmann method which evolves the coupled momentum and thermal
equations and includes a reactive term. We tune the parameters affecting flame
properties, in order to address the competition between turbulent mixing and
reaction, ranging from slow to fast-reaction rates. We also study the mutual
feedback between turbulence evolution driven by the Rayleigh-Taylor instability
and front propagation against gravitational acceleration. We quantify both the
enhancement of flame propagation due to turbulent mixing for the case of slow
reaction-rate as well as the slowing down of turbulence growth for the fast
reaction case, when the flame quickly burns the gravitationally unstable phase.
An increase of intermittency at small scales for temperature characterizes the
case of fast reaction, associated to the formation of sharp wrinkled fronts
separating pure hot/cold fluids regions.
