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

Bees, M. A. and Hill, N. A. (1998) Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms Journal of Mathematical Biology, 38 (2). pp. 135-168. ISSN 0303-6812

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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.

Item Type: Article
Additional Information: This is a pre-copy-editing, author-prepared, peer-reviewed PDF of an article published in Journal of Mathematical Biology, 38, 135-168. © 1999 Springer. Click here to access the publisher's version.
Uncontrolled Keywords: Bioconvection patterns, Swimming micro-organisms, Gyrotaxis, Travelling waves, Fokker, Planck equation, Amplitude equation
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1432

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