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Fisher equation with turbulence in one dimension. (English) Zbl 1180.37126
Summary: As an example of life at high Reynolds number, 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 remarkably long persistence times), sinks in the turbulent field. An important consequence is a large reduction in the carrying capacity of the fluid medium. We analytically determine the regimes where this quasi-localized behavior occurs and test our predictions by numerical simulations.

MSC:
37N25 Dynamical systems in biology
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76F35 Convective turbulence
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
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