Pattern formation in localized photo-bioconvection

Many photosynthetic micro-organisms are able to detect light and move towards optimal light intensities, an ability known as phototaxis. In suspensions of phototatic micro-algae Chlamydomonas Reinhardtii, it was demonstrated that using a thin localized light beam to attract and accumulate cells could induce macroscopic recirculation flows referred to as localized photo-bioconvection flows. Here, we study the associated concentration patterns. The cells being slightly denser than their surrounding fluid, bioconvection originates from spatial gradients of cell concentration which create density inhomogeneities. A dimensionless Rayleigh number compares buoyancy-driven convection over diffusion. While spontaneous (without light excitation) bioconvection occurs in suspensions of on average upward swimming micro-organisms only above a critical Rayleigh number, it was shown that localized photo-bioconvection occurs below this threshold. In the present study, we show that when the beam width is wider than the suspension depth, the concentration field exhibits remarkable symmetry breakings.