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

Active turbulence in overdamped chiral systems presents a complex challenge, namely the frequent exhibition of non-universal spectral scaling, creating large-scale coherent structuring that seemingly defy 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 Renormalised 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 particle distributions consistently exhibit steep, dissipative energy spectra, associated with enstrophy injection at the microscale, the RFE-filtered field reveals a dual behavior characterized by an inverse energy cascade. Under conditions of high intrinsic activity, or frustration, 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.