Turbulent front speed in the Fisher equation: dependence on Damkohler number

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.