We develop a formal and numerical spectral analysis for U (1) symmetry-breaking quantum fluids suitable for analyzing turbulent flows, with specific application to the Gross-Pitaevskii fluid. Our formulation establishes the connection between energy spectral densities, velocity power spectra, and two-point spatial correlation functions for compressible quantum fluids. Removing binning approximations, and adding flexibility to k-space evaluation, the formulation allows for high resolution spectral analysis and reconstruction of correlation functions. A single vortex in a trapped planar BEC provides an analytically tractable example with spectral features of interest in both the infrared and ultraviolet regimes. Vortex distributions spanning the dipole gas, plasma, and clustered phases exhibit increased velocity coherence length with increasing vortex energy.

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