Complex network analysis of the gravity effect on premixed flames propagating in a Hele-Shaw cell

We study the effect of gravity on spatiotemporal flame front dynamics in a Hele-Shaw cell from the viewpoint of complex networks. The randomness in flame front dynamics significantly increases with the gravitational level when the normalized Rayleigh number R_{a} is negative. This is clearly identified by two network entropies: the flame front network entropy and the transition network entropy. The irregular formation of large-scale wrinkles driven by the Rayleigh-Taylor instability plays an important role in the formation of high-dimensional deterministic chaos at R_{a}<0, resulting in the increase in the randomness of flame front dynamics.