Gyrotactic plume formation and bioconvection

Many microorganisms are motile, that is, they swim. Some motile micro-organisms (swimmers), such as the micro-algae Chlamydomonas augustae (née nivalis), navigate towards the upper surface by being bottom-heavy. In a downflowing pipe, the balance between the gravitational and viscous torque causes the micro-organism to swim towards the centre, forming a focused beam-like structure. This sideway drift of bottom-heavy swimmers is known as gyrotaxis. Gyrotaxis is responsible for many naturally occurring phenomena, such as bioconvection, micro-patchiness and the formation of thin phytoplankton layers in some parts of the ocean.

In a series of work, we model different pattern formations due to gyrotaxis, and compare various continuum model for the swimmer phase. Our first publication compare the consequences of the popular model by Pedley & Kessler with the more accurate model based on the generalized Taylor dispersion theory in the formation of gyrotactic plume. We found that the Pedley & Kessler model overestimates the swimmer’s effective dispersion, which results in a steady plume profile that is not physical. Instead, the gyrotactic plume should be considered as a singular structure that tends to blow up in finite time, as explained by our later work. Subsequently, the formation of blips (blobs of swimmers formed from the plume at later stages) should be considered as a streamwise instability on a developing plume profile instead of a steady profile.

Our second publication considers the consequence of the geometry of the container. Suprisingly, the cylindrical shape of the container give rises to a sequence of transcritical bifurcation from the uniform state, which corresponds to the bioconvective instability. These subcritical bifurcations are in contrast to the supercriticla pitchfork bifurcations previous found in two-dimensional analysis, highlighting the importance of geometry in the pattern formation.