Fisher equation with turbulence in one dimension

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Benzi, Roberto
Nelson, David R.
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Abstract
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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.
Comment: 15 pages
Keywords
Quantitative Biology - Populations and Evolution, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Chaotic Dynamics
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