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

TL;DR

This paper investigates how turbulent flow influences reactive front propagation in the Fisher equation, revealing that turbulence can saturate front speed and that reaction nonlinearity slightly accelerates it, using simulations and mean-field theory.

Contribution

It introduces a mean-field model incorporating turbulent diffusion memory effects to estimate front speed at high Damkohler numbers, validated by direct numerical simulations.

Findings

Turbulent diffusion causes front speed saturation at turbulent flow speeds.

Effective correlation time in reactive flows is shorter than in non-reactive flows.

Reaction nonlinearity slightly increases front speed.

Abstract

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.