Thin front propagation in random shear flows

Abstract

Front propagation in time-dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts--i.e., the so-called geometrical optics limit. In particular, we consider fronts stirred by random shear flows, whose time evolution is modeled in terms of Ornstein-Uhlembeck processes. We show that the ratio between the time correlation of the flow and an intrinsic time scale of the reaction dynamics (the wrinkling time tw) is crucial in determining both the front propagation speed and the front spatial patterns. The relevance of time correlation in realistic flows is briefly discussed in light of the bending phenomenon--i.e., the decrease of propagation speed observed at high flow intensities.