  Direct numerical simulations and mean-field theory are used to model reactive
front propagation in a turbulent medium. In the mean-field approach, memory
effects of turbulent diffusion are taken into account to estimate the front
speed in cases when the Damkohler number is large. This effect is found to
saturate the front speed to values comparable with the speed of the turbulent
motions. By comparing with direct numerical simulations, it is found that the
effective correlation time is much shorter than for non-reacting flows. The
nonlinearity of the reaction term is found to make the front speed slightly
faster.
