Fisher equation with turbulence in one dimension

Roberto Benzi; David R. Nelson

doi:10.1016/j.physd.2009.07.015

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arXiv · 0902.0313

Fisher equation with turbulence in one dimension

Roberto Benzi·David R. Nelson

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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.

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Roberto Benzi, David R. Nelson. 2009-02-02. Fisher equation with turbulence in one dimension. https://doi.org/10.1016/j.physd.2009.07.015

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