Front induced feedback in convective flowfields

We numerically study the feedback between a propagating front and the underlying flowfield for a range of different parameters. The flowfields are generated by a modified form of the Boussinesq equation, which generates counter rotating convection rolls in a long shallow layer of fluid. The strength of the convection rolls is quantified by the Rayleigh number. In many reaction-advection-diffusion systems, a difference in buoyancy between the products and the reactants creates secondary fluid rolls which interact with the existing convection rolls and affect the velocity and geometry of the propagating front and the underlying flowfield. This roll formed due to the backaction of the front on the flowfield also affects the geometry of the front interface, noticeably making it more tilted and stretched. We quantify the strength of this backaction roll by a quantity called the solutal Rayleigh number, which is related to the ratio of the buoyancy difference between the products and the reactants to the diffusion coefficient of the products. We investigate the interaction of this front induced backaction roll and the convection rolls in two dimensional cellular flow and for three dimensional spatiotemporally chaotic flow.