  Bioconvection is the prototypical active matter system for hydrodynamic
instabilities and pattern formation in suspensions of biased swimming
microorganisms, particularly at the dilute end of the concentration spectrum
where cell-cell interactions typically are neglected. Confinement is an
inherent characteristic of such systems, including those that are
naturally-occurring or industrially-exploited, so it is important to understand
the impact of boundaries on the hydrodynamic instabilities. Despite recent
interest in this area we note that commonly-adopted symmetry assumptions in the
literature, such as for a vertical channel or pipe, are uncorroborated and
potentially unjustified. Therefore, by employing a combination of analytical
and numerical techniques, we investigate whether confinement itself can drive
asymmetric plume formation in a suspension of bottom-heavy swimming
microorganisms (gyrotactic cells). For a class of solutions in a vertical
channel we establish the existence of a first integral of motion, and reveal
that asymptotic asymmetry is plausible. Furthermore, numerical simulations from
both Lagrangian and Eulerian perspectives demonstrate with remarkable agreement
that asymmetric solutions can indeed be more stable than symmetric; asymmetric
solutions are in fact dominant for a large, practically-important region of
parameter space. In addition, we verify the presence of blip and varicose
instabilities for an experimentally accessible parameter range. Finally, we
extend our study to a vertical Hele-Shaw geometry to explore whether a simple
linear drag approximation can be justified. We find that although
two-dimensional bioconvective structures and associated bulk properties have
some similarities with experimental observations, approximating near wall
physics in even the simplest confined systems remains challenging.
