Fragility of reaction-diffusion models to competing advective processes

Abstract: We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that the front dynamics can be described by an FKPP-like equation only at sufficiently fast diffusion or large coupling strength. For such parameter regimes, we find a mapping to an effective FKPP equation. We also find that FKPP equation is fragile with respect to the coupling to an advection-only mechanism, discover conditions when the front width diverges, and when front speed is insensitive to the coupling. At zero diffusion in this mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.