  Dense systems of active matter exhibit highly dynamic collective motion
characterized by intermingled vortices, referred to as active turbulence. The
interaction between these vortices is key to controlling turbulent dynamics,
and a promising approach for revealing the rules governing their interaction is
geometric confinement. In this study, we investigate the vortex-pairing
patterns in confined bacterial suspensions as a model frustrated system in
which a perfect antiferromagnetic state is prohibited. We found that three-body
vortex interactions exhibited anomalous pairing-order transition from
co-rotational vortex-pairing to counter-rotating patterns with frustration.
Although an active matter system is in non-equilibrium, our theory based on
bending energy accounts for significant features including pattern transition
and shift of the transition point in frustrated systems. Moreover, the
interplay between the chirality in collective motion and frustration in vortex
pairing creates a collective rotational flow under the broad geometric
conditions of a confined space. Our results show that frustrated vortex
patterning promotes a geometric approach for arranging active turbulence in
microfluidic systems.
