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Dense systems of active matter exhibit a highly dynamic collective motioncharacterized by intermingled vortices, referred to as active turbulence. Theinteraction between these vortices is a key to controlling turbulent dynamics,and one promising approach to revealing the rules governing their interactionis through geometric confinement. In this study, we investigate the vortexpairing patterns in confined bacterial suspensions as a model frustrated systemwhere a perfect antiferromagnetic state is not allowed. We find that three-bodyvortex interactions show anomalous pairing order transition from co-rotationalvortex pairing to the counter-rotating pattern with frustration. Although theactive matter system is non-equilibrium, our theory based on bending energyaccounts for the significant features including pattern transition and theshift of the transition point in frustrated systems. Moreover, the interplay ofchirality in collective motion and frustration in vortex pairing createscollective rotational flow in broad geometric conditions of confined space. Ourresults illustrate that the use of frustrated vortex patterning promotes ageometric approach to arranging active turbulence in microfluidic systems.

Geometric frustration and pairing order transition in confined bacterial vortices