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

Bees, M. and Hill, N. (1999) Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms. Journal of Mathematical Biology, 38(2), pp. 135-168.

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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Hill, Professor Nicholas and Bees, Dr Martin
• Authors: Bees, M., and Hill, N.
• Subjects: Q Science > QA Mathematics; Q Science > QH Natural history > QH301 Biology
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Mathematical Biology
• Journal Abbr.: J. math. biol.
• Publisher: Springer
• ISSN: 0303-6812
• ISSN (Online): 1432-1416
• Copyright Holders: Copyright © 1999 Springer
• First Published: First published in Journal of Mathematical Biology 1999 38(2):135-168
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher