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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 26 May 1997 / Revised version: 10 May 1998
Rights and permissions
About this article
Cite this article
Bees, M., Hill, N. Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms. J Math Biol 38, 135–168 (1999). https://doi.org/10.1007/s002850050144
Issue Date:
DOI: https://doi.org/10.1007/s002850050144