Journal of Mathematical Biology

, Volume 38, Issue 2, pp 135-168

Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms

  • M. A. BeesAffiliated withDepartment of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
  • , N. A. HillAffiliated withDepartment of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

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Abstract.

 The non-linear structure of deep, stochastic, gyrotactic bioconvection is explored. A linear analysis is reviewed and a weakly non-linear analysis justifies its application by revealing the supercritical nature of the bifurcation. An asymptotic expansion is used to derive systems of partial differential equations for long plume structures which vary slowly with depth. Steady state and travelling wave solutions are found for the first order system of partial differential equations and the second order system is manipulated to calculate the speed of vertically travelling pulses. Implications of the results and possibilities of experimental validation are discussed.

Key words: Bioconvection patterns Swimming micro-organisms Gyrotaxis Travelling waves Fokker Planck equation Amplitude equation