Fragility of reaction-diffusion models to competing advective processes

TL;DR

This paper investigates how the addition of an advection process affects the behavior of reaction-diffusion models, revealing conditions under which the models remain robust or become fragile, with implications for understanding front dynamics.

Contribution

It demonstrates the fragility of FKPP reaction-diffusion models when coupled with advection, identifying regimes where the models can be effectively mapped or become unstable.

Findings

Front dynamics are FKPP-like only at high diffusion or strong coupling.

The FKPP equation is fragile to advection coupling, with diverging front width.

Downwind front speed remains finite at zero diffusion as coupling vanishes.

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.