  Squirmers that are bottom-heavy experience a torque that aligns them along
the vertical so that they swim upwards. In a suspension of many squirmers, they
also interact hydrodynamically via flow fields that are initiated by their
swimming motion and by gravity. Swimming under the combined action of flow
field vorticity and gravitational torque is called gyrotaxis. Using the method
of multi-particle collision dynamics, we perform hydrodynamic simulations of a
many-squirmer system floating above the bottom surface. Due to gyrotaxis they
exhibit pronounced cluster formation with increasing gravitational torque. The
clusters are more volatile at low values but compactify to smaller clusters at
larger torques. The mean distance between clusters is mainly controlled by the
gravitational torque and not the global density. Furthermore, we observe that
neutral squirmers form clusters more easily, whereas pullers require larger
gravitational torques due to their additional force-dipole flow fields. We do
not observe clustering for pusher squirmers. Adding a rotlet dipole to the
squirmer flow field induces swirling clusters. At high gravitational strengths,
the hydrodynamic interactions with the no-slip boundary create an additional
vertical alignment for neutral squirmers, which also supports cluster
formation.
