Axisymmetric Bioconvection in a Cylinder

In three-dimensional bioconvection, the regions of rising and sinking fluid are dissimilar. This geometrical effect is studied for axisymmetric bioconvection in a cylindrical cell with stress-free (i.e. normal velocity and tangential stress vanish) lateral and top boundaries, and rigid bottom boundary. Using the continuum model of Pedley et al. (1988, J. Fluid Mech.195, 223–237) for bioconvection in a suspension of swimming, gyrotactic microorganisms, the structure and stability of an axisymmetric plume in a deep chamber 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. Comparisons are made with two-dimensional bioconvection.