The E ect of Finite Front Thickness on the Enhanced Speed of Propagation

Recently, Majda and Souganidis have presented a rigorous asymptotic theory governing the large-scale renormalized ame front dynamics for a convection-reaction-di usion system involving KPP type chemistries and small scale turbulence. This theory is valid in the context of an in nitely thin reaction layer. Embid, Majda, and Souganidis have explored this rigorous theory within the context of a shear layer geometry, and demonstrate that the enhanced burning speed is sensitively dependent upon the presence of a mean wind transverse to the direction of the ame propagation. Here, we address the e ect that a thin reaction layer may have on the enhanced ame propagation for the case of a small scale shear layer with and without a transverse mean wind. We show through high resolution, two dimensional numerical simulations that the enhanced burning speed is sensitively dependent on the presence of a transverse mean wind in a qualitatively similar fashion to the asymptotic theory; but further, we exhibit that a nite reaction zone yields e ective burning speeds which are smaller than the theoretical predictions for in nitely thin ame fronts.