We report numerical evidence for a wave-turbulent regime in dense suspensions of active phoretic disks with physicochemical hydrodynamic interactions. At low activity, the disks assemble into active Wigner solids, which melt into a hexatic phase with increasing activity. This phase transition in dense suspensions is accompanied by the destruction of standing waves in the solid phase and the onset of turbulent dynamics in the hexatic phase. Unlike canonical active turbulence typically characterized by large-scale advection of self-propelling constituents, our disks remain caged and perform local vibrations. This behavior mirrors the weak turbulence of bending waves in vibrating elastic plates. Moreover, the observed turbulence displays a self-similar, power-law energy spectrum at large wavenumbers, scale-dependent spatial intermittency but weak temporal intermittency, and statistically weak nonlinearity, consistent with reported signatures of wave turbulence. We therefore identify a new wave turbulence regime in active matter’s hexatic phase, which we call active wave turbulence.

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• Collective behavior
• Emergence of patterns
• Low Reynolds number swimmers
• Microswimmers
• Phase transitions
• Collective dynamics
• Direct numerical simulations
• Immersed boundary methods
• Lattice-Boltzmann methods
• Navier-Stokes equation
• Stokes equations