Fisher equation with turbulence in one dimension

TL;DR

This paper studies how turbulence affects the spread of microorganisms in a one-dimensional medium, revealing that strong turbulence causes bacteria to become quasi-localized, significantly reducing the environment's carrying capacity.

Contribution

It analytically and numerically demonstrates the conditions under which turbulence induces quasi-localization of microorganisms in the Fisher equation.

Findings

Strong turbulence leads to bacteria tracking sinks in the turbulent field.

Quasi-localization results in a significant decrease in carrying capacity.

Analytical regimes for localization are confirmed by numerical simulations.

Abstract

We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimension subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria, for example, track in a quasilocalized fashion (with remakably long persistance times) sinks in the turbulent field. An important consequence is a large reduction in the carrying capacity of the fluid medium. We determine analytically the regimes where this quasi-localized behavior occurs and test our predictions by numerical simulations.