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Wavelength Selection in Gyrotactic Bioconvection

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Abstract

We investigate pattern formation by swimming micro-organisms (bioconvection), when their orientation is determined by balance between gravitational and viscous torques (gyrotaxis), due to being bottom heavy. The governing equations, which consist of the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation, are solved numerically in a large cross section chamber with periodic boundary conditions in the horizontal directions. The influence of key parameters on wavelength selection in bioconvection patterns is investigated numerically. For realistic ranges of parameter values, the computed wavelengths are in good agreement with the experimental observations provided that the diffusion due to randomness in cell swimming behaviour is small, refuting a recently published claim that the mathematical model becomes inaccurate at long times. We also provide the first computational evidence of “bottom-standing” plumes in a three-dimensional simulation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

    S. Ghorai

  2. Department of Mathematics, Central University of Himachal Pradesh, Dharamsala, India

    R. Singh

  3. School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

    N. A. Hill

Authors
  1. S. Ghorai
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  2. R. Singh
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  3. N. A. Hill
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Correspondence to S. Ghorai.

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Ghorai, S., Singh, R. & Hill, N.A. Wavelength Selection in Gyrotactic Bioconvection. Bull Math Biol 77, 1166–1184 (2015). https://doi.org/10.1007/s11538-015-0081-9

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  • DOI: https://doi.org/10.1007/s11538-015-0081-9

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