Rayleigh-Taylor Unstable Flames: the Coupled Effect of Multiple Perturbations

The Rayleigh-Taylor (RT) instability is important in the fields of aerospace engineering, nuclear physics, and astrophysical research, particularly in studies of Type Ia supernovae. In some applications, the RT instability is complicated by a reaction at the unstable interface. In this paper, we show how this reaction changes the behavior of the RT instability. Using 2D direct numerical simulations (DNS) of Boussinesq premixed flames with a model reaction rate, we show how the flame responds to three types of perturbation: a large amplitude single mode primary perturbation, a smaller amplitude single mode secondary perturbation, and a numerically generated system perturbation with both single mode and multimode components. Early on, the evolution of the flame is dominated by the primary perturbation and, differently from single mode nonreacting RT, the flame propagates as a metastable traveling wave in the form of bubbles separated by cusp-like spikes. However, the lifetime of this traveling wave depends on the properties of the secondary and system perturbations and on the strength of gravity. Once the traveling wave is destabilized, the flame front bubbles rapidly grow to large scales. We identify five distinct flame growth solution types, with the symmetry and properties of each depending on the balance and interactions between the three types of perturbation. In particular, we show that the primary and secondary modes can couple to generate a tertiary mode which ultimately dominates the flow. Depending on the wavenumber of the tertiary mode, the flame may stall, develop coherent pulsations, or even become a metastable traveling wave again, behaviors not seen in nonreacting RT.Comment: 25 pages, 15 figures; Submitted to: Physical Review Fluids; Code and Data Release: see https://doi.org/10.5281/zenodo.834691