Parametrizing the burning speed enhancement by small-scale periodic flows: I. Unsteady shears, flame residence time and bending

We document and explain the existence of two distinct scaling regimes for the burning speed enhancement of an idealized premixed flame as a result of its distortion by an unsteady periodic shear. The simplified model used in the present study allows for a rigorous, quantitative explanation of the bending in the scaling exponent, either linear or sublinear in the shear intensity, in terms of a non-dimensional flame residence time which compares the intrinsic time-scale of the unsteady flow with time it takes the corresponding steady shear to fully distort a flame. It is the non-trivial dependence of this latter flame wrinkling time with respect to the shear intensity that leads to the scaling behaviour. A combination of asymptotic analysis and high-resolution numerical simulations is used to validate the enhancement parametrization of both standing- and travelling-wave solutions for the perturbed front.