Rayleigh–Taylor instability of pulled versus pushed fronts

Due to a possible density difference across an autocatalytic reaction–diffusion front, a hydrodynamic Rayleigh–Taylor instability triggering fingering of the self-organized interface can set in when the front is propagating perpendicularly to the gravity field. We investigate here the influence of the form of the reaction kinetics on the stability properties and the nonlinear dynamics of fingering. We show that the pulled versus pushed character of the front leads to important differences in the dispersion curves and in the role of fluctuations in the nonlinear dynamics of fingering. In particular, the effective dispersion curve in the pulled regime is strongly time-dependent, and only converges to the usual dispersion relation of the Rayleigh–Taylor instability at late times. Our results also have implications for combustion fronts.