Nonlinear hydrodynamic corrections to supersonic F–KPP wave fronts

Abstract

We study the hydrodynamic corrections to the dynamics and structure of an exothermic chemical wave front of Fisher–Kolmogorov–Petrovskii–Piskunov (F–KPP) type which travels in a one-dimensional gaseous medium. We show in particular that its long time dynamics, cut-off sensitivity and leading edge behavior are almost entirely controlled by the hydrodynamic front speed correction δ U h which characterizes the pushed nature of the front. Reducing the problem to an effective comoving heterogeneous F–KPP equation, we determine two analytical expressions for δ U h : an accurate one, derived from a variational method, and an approximate one, from which one can assess the δ U h sensitivity to the shear viscosity and heat conductivity of the fluid of interest.