“…In the following, we assume that the flame behaves as a fractal surface at all stages of its development, as suggested by various models and analysis [23,28,49,[54][55][56][57][58][59][60][61][62][63][64][65]. Once derived the balance equations describing the evolution of a statistically one-dimensional flame evolving in an homogenous and isotropic frozen turbulence (Section 2), exact closures are proposed to fit this requirement (Section 3) while the influence of two sub-grid scale models, a simple algebraic model and its dynamic version, on resolved and total flame surfaces, and then on the overall turbulent flame speed, as well as the unsteady flame response, are discussed in Section 4, including model parameter uncertainties.…”