Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth

Hill, N.A. , Pedley, T.J. and Kessler, J.O. (1989) Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth. Journal of Fluid Mechanics, 208, pp. 509-543. (doi: 10.1017/S0022112089002922)

88747.pdf - Published Version


Publisher's URL:


The effect of gyrotaxis on the linear stability of a suspension of swimming, negatively buoyant micro-organisms is examined for a layer of finite depth. In the steady basic state there is no bulk fluid motion, and the upwards swimming of the cells is balanced by diffusion resulting from randomness in their shape, orientation and swimming behaviour. This leads to a bulk density stratification with denser fluid on top. The theory is based on the continuum model of Pedley, Hill & Kessler (1988), and employs both asymptotic and numerical analysis. The suspension is characterized by five dimensionless parameters: a Rayleigh number, a Schmidt number, a layer-depth parameter, a gyrotaxis number G, and a geometrical parameter measuring the ellipticity of the micro-organisms. For small values of G, the most unstable mode has a vanishing wavenumber, but for sufficiently large values of G, the predicted initial wavelength is finite, in agreement with experiments. The suspension becomes less stable as the layer depth is increased. Indeed, if the layer is sufficiently deep an initially homogeneous suspension is unstable, and the equilibrium state does not form. The theory of Pedley, Hill & Kessler (1988) for infinite depth is shown to be appropriate in that case. An unusual feature of the model is the existence of overstable or oscillatory modes which are driven by the gyrotactic response of the micro-organisms to the shear at the rigid boundaries of the layer. These modes occur at parameter values which could be realized in experiments.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Hill, Professor Nicholas
Authors: Hill, N.A., Pedley, T.J., and Kessler, J.O.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Journal Abbr.:J. Fluid Mech.
Publisher:Cambridge University Press
ISSN (Online):1469-7645
Copyright Holders:Copyright © 1989 Cambridge University Press
First Published:First published in Journal of Fluid Mechanics 208:509-543
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

University Staff: Request a correction | Enlighten Editors: Update this record