Signatures of Coherent Vortex Structures in a Disordered 2D Quantum Fluid

The emergence of coherent rotating structures is a phenomenon characteristic of both classical and quantum 2D turbulence. In this work we show theoretically that the coherent vortex structures that emerge in decaying 2D quantum turbulence can approach quasi-classical rigid-body rotation, obeying the Feynman rule of constant average areal vortex density while remaining spatially disordered. By developing a rigorous link between the velocity probability distribution and the quantum kinetic energy spectrum over wavenumber $k$, we show that the coherent vortex structures are associated with a $k^3$ power law in the infrared region of the spectrum, and a well-defined spectral peak that is a physical manifestation of the largest structures. We discuss the possibility of realizing coherent structures in Bose--Einstein condensate experiments and present Gross-Pitaevskii simulations showing that this phenomenon, and its associated spectral signatures, can emerge dynamically from feasible initial vortex configurations.