Bifurcation and Stability of plumes in a downflowing gyrotactic microorganism suspensions in a vertical cylindrical pipe

Experiments by Kessler (1986, J. Fluid Mech. 173:191–205) have shown that in a suspension of downflowing gyrotactic swimming microalgae, the cells form a beam-like structure (plumes). Such a structure is prone to an axisymmetric blip instability. To better understand the blip instability, a three-dimensional stability analysis is performed in a circular pipe flow by extending the previous analysis of two-dimensional channel flow (Hwang & Pedley, 2014, J. Fluid Mech. 749:750-777). It is found that under the axisymmetric and streamwise-invariant assumption, there can be multiple branches of steady solutions for the gyrotactic plume. Their respective stability is computed, and the unstable mode is consistent with the blips observed in gyrotactic plumes.