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Kinetic Turing Instability and Emergent Spectral Scaling in Chiral Active Turbulence

The spontaneous emergence of coherent structures from chaotic backgrounds is a hallmark of active biological swarms. We investigate this self-organization by simulating an ensemble of polar chiral active agents that couple locally via a Kuramoto interaction. We demonstrate that the system's transition from chaos to active turbulence is characterized by quantized loop phase currents and coherent clustering, and that this transition is strictly governed by a kinetic Turing instability. By deriving the continuum kinetic theory for the model, we identify that the competition between local phase-locking and active agent motility selects a critical structural wavenumber. The instability then drives the system into a state of developed, active turbulence that exhibits stable, robust power-laws in spectral density, suggestive of universality and consistent with observations from a broad range of turbulent phenomena. Our results bridge the gap between discrete chimera states and continuous fluid turbulence, suggesting that the statistical scaling laws of active turbulence can arise from fundamental kinetic instability criteria.