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Renormalized hydrodynamics in polar chiral active matter: Spectral scaling and disorder-driven vortex clustering in phase-coupled, motile oscillators

Magnus F. Ivarsen*,†

  • *Also at The European Space Agency Centre for Earth Observation, Frascati, Italy.
  • †Contact author: magnus.fagernes@gmail.com
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APS Open Sci. 1, 000135 – Published 15 September, 2026

DOI: https://doi.org/10.1103/hc9d-fpmj

Abstract

Active turbulence in overdamped chiral systems presents a complex challenge, namely, the frequent exhibition of nonuniversal spectral scaling, creating large-scale coherent structuring that seemingly defies standard inertial fluid descriptions. In this study, we investigate the hydrodynamic limit of a two-dimensional polar chiral active fluid modeled as an ensemble of locally coupled, motile Kuramoto-Sakaguchi oscillators. By introducing a renormalized fluid element (RFE) operator, we coarse-grain microscopic phase singularities, and in so doing, we isolate the macroscopic transport dynamics. We demonstrate that while the raw phase field consistently exhibit a steep, dissipative energy spectrum, associated with enstrophy injection at the microscale, the RFE-filtered field reveals a dual behavior characterized by an inverse energy cascade. When the intrinsic frequency dispersion, drawn from a scale-free power-law distribution, is broad enough to seed fluctuations at all resolved scales, this hidden cascade acts akin to a topological heat pump, driving the system toward a state of macroscopic vortex clustering, structurally analogous to supersonic shallow water dynamics. Conversely, a narrow frequency dispersion results in kinetic arrest, forming an active vortex glass. These results suggest that overdamped phase-slaved active matter can sustain effective inertial cascades, providing a mathematical framework for understanding scale-dependent energy transport in driven chiral systems.

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Polar chiral active matter as a motile, disordered Josephson array: Information supercurrents and Goldstone spin waves

Magnus F Ivarsen
Phys. Rev. E 114, 035417 (2026)

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APS Open Sci. 1, 000135– Published 15 September, 2026
Vol. 1
  • Received 9 December 2025
  • Revised 7 April 2026
  • Accepted 23 July 2026
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