Mean cell wavelengths of wrinkled premixed flames in weak gravity fields: spontaneous evolutions

Starting from a Rakib–Sivashinsky type of equation for the local amplitude of wrinkling of premixed flames propagating upward or downward, we numerically study how the ensemble-averaged cell wavelengths (crest-to-crest, or from spectral density of wrinkling) evolve from random initial conditions, when the gravity is weak. Tentative theories yield simple scaling laws that are in good agreement with the numerical results; yet some lack of universality suggests that such laws are merely accurate and not exact. Open problems, e.g. relating to noise, are finally evoked.