  Kessler (Nature, vol. 313, 1985, pp. 218-220) first showed that plume-like
structures spontaneously appear from both stationary and flowing suspensions of
gyrotactic microswimmers in a vertical pipe. Recently, it has been shown that
there exist multiple numbers of steady axisymmetric axially uniform solutions
to such a system (Bees, M. A. & Croze, O. A., Proc. R. Soc. A., vol. 466, 2010,
pp. 2057-2077). In the present study, we generalise this finding by reporting
that a countably infinite number of such solutions emerge as Richardson number
increases. Linear stability, weakly nonlinear and fully nonlinear analyses are
performed, revealing that each of the solutions arises from the destabilisation
of uniform suspension. The discrete number of the solutions is due to the
finite flow domain, while the transcritical nature of the bifurcation is
because of the cylindrical geometry which breaks the horizontal symmetry of the
system. It is further shown that there exists a maximum threshold of achievable
downward flow rate for each solution if the flow is to remain steady, as
varying the pressure gradient can no longer increase the flow rate from the
solution. Except the one arising at the lowest Richardson number, all of the
solutions found are unstable, implying that they would play a role in the
transient dynamics in the route from a uniform suspension to the
fully-developed gyrotactic pattern.
