Evolution of bioconvection patterns in a culture of motile flagellates

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Abstract
Numerical experiments were carried out on the pattern formation of bioconvection that is observed in cultures of motile aquatic microorganisms. New features were revealed on how the bioconvective system evolves and how the number of falling fingers is selected at each stage of evolution. At the onset of convection, the relevant dynamical regime is that of the Rayleigh–Taylor instability. Then, readjustment of the wavenumber occurs as the adjacent convection cells combine with each other. The trajectory in (total kinetic energy, total potential energy) space shows that evolution of the system proceeds in the direction of intensifying the downward advection of microorganisms and reducing the total potential energy of the system. Finally the system reaches a stationary state, where the aspect ratio of the convection cells resembles that of Bénard–Rayleigh convection and is optimum for the efficient downward advection of microorganisms. Furthermore, it is demonstrated that trajectories of the two cases deviate from this major evolution. In the case where the diffusion time of the system is large, the system shows remarkable oscillation and repeats the Rayleigh–Taylor instability intermittently. In the case where the viscous effect is large, the system ceases to evolve before reaching the optimum mode.