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.