Bioconvection of gravitactic microorganisms in a vertical cylinder

Patterns formation of gravitactic microorganism in a vertical cylinder is described by the Navier-Stokes equation coupled with the microorganism conservation equation. The control volume method is used to solve numerically these equations. It is found that when the Peclet number is decreased, the critical Rayleigh number also decreases to approach the value corresponding to Bénard convection under fixed-flux heating condition. However, at high Peclet numbers, the development convection is very different from that of Bénard convection. The most fundamental difference is that, while Bénard convection is a supercritical instability, the gravitactic bioconvection is shown to be a subcritical bifurcation from the diffusion state.