Using the continuum model of Pedley, Hill & Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results.

Using the continuum model of Pedley et al. ͓J. fluid Mech. 195, 223 ͑1988͔͒ for bioconvection in a suspension of swimming, gyrotactic microorganisms , the existence and stability of periodic arrays of two-dimensional plumes in deep chambers are investigated. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a microorganism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plumes are sometimes unstable to varicose or meandering modes. A linear stability analysis for an infinitely deep plume predicts the growth rates of these instabilities and agrees well with the numerical results.

Bioconvection occurs as the result of the collective behaviour of many microorganisms swimming in a fluid and is realized as patterns similar to those of thermal convection which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. The continuum model of Pedley et al. (1988, J. Fluid. Mech. 195, 223-237) is used to describe the suspension. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. To examine the dependence of the horizontal pattern wavelengths on the parameters, we consider two-dimensional solutions in a wide chamber using rigid side walls. The wavelengths of the numerical computations are in good agreement with the experimental observations and we provide the first computational examples of the commonly seen 'bottom-standing' plumes.

Phototaxis is a directed swimming response toward a light source sensed by micro-organisms. Positive phototaxis represents swimming toward the source of light intensity and negative phototaxis is the swimming away from it. In this paper we develop a new model for phototaxis that incorporates the effects of absorption and scattering by the micro-organisms. This model is then used to analyze the linear stability of a suspension of phototactic algae illuminated by a collimated radiation at the top. A comprehensive numerical study of the linear stability is presented with particular emphasis on the scattering effect. As a result of scattering, for some parameter values, the micro-organisms accumulate in two horizontal layers at different depths in the basic equilibrium state. Examples of oscillatory instabilities are also found.

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