Short-term prediction of a propagating flame in a Hele-Shaw cell

We numerically study the dynamic behavior of flame front fluctuations in a Hele-Shaw cell by solving a nonlinear evolution equation describing a downwardly propagating flame dynamics, including the short-term predictability of flame front fluctuations. Our recent study [Y. Nomi et al., Phys. Rev. E, vol. 103, p. 022218, 2021] has reported the two important findings under the negative normalized Rayleigh number conditions: (i) the randomness in flame front fluctuations significantly increases with the gravitational level, and (ii) 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. The effect of additive noise on the randomness in flame front dynamics and the cell size distribution of the wrinkles has been clarified in our subsequent study [Y. Nomi et al., Chaos, vol. 31, p. 123133, 2021]. The most interesting result in the present study is that the flame front fluctuations can be sufficiently predicted by a reservoir computing [T. Tokami et al., Phys. Rev. E, vol. 101, p. 042214, 2020]. In this presentation, we will discuss the relevance of the predictability nature to the identification of deterministic chaos.