Cellular flames may exhibit a non-modal transient instability

In this work, an integrodifferential equation modeling the Darrieus-Landau instability of plane flame fronts was analyzed numerically. Our numerical experiments confirm formation of a steady cellular-like structure associated with the steady coalescent pole solutions to the Sivashinsky equation on the surface of small enough flames of size L < L-c. However, within the considered computational times, a steady limiting shape of the flame front was not reached for large enough flames of size L > L-c. Instead, a smooth surface of an almost steadily shaped flame is repeatedly disturbed by perturbations, resembling small cusps, appearing randomly in time. The nature of these small cusps was studied. In particular, the correlation between the critical length L, and parameters of the computational algorithm and the computer precision was investigated. Rates of the linear transient growth of perturbations of the steady coalescent pole solutions to the Sivashinsky equation have been estimated by means of the analysis of the pseudospectra of the associated linear operator. The results support the idea of high sensitivity of cellular flames to the external noise by linking it with the non-modal instability of the steady coalescent pole solutions to the Sivashinsky equation.