Anomalous energy injection in the Gross-Pitaevskii framework for turbulence in neutron star glitches

Neutron star glitches -- sudden increases in rotational frequency -- are thought to result from angular momentum transfer via quantized vortices in the superfluid core. To investigate the underlying superfluid dynamics, we employ a two-dimensional rotating atomic Bose-Einstein condensate described by a damped Gross-Pitaevskii equation with an imposed pinning potential that serves as a simplified analogue of a crust. Within this minimal framework, we examine the emergence and evolution of turbulent vortex motion following impulsive perturbations reminiscent of glitch-like forcing. Our simulations reveal a transient Kolmogorov-like turbulent cascade ($k^{-5/3}$) that transitions to a Vinen-like scaling ($k^{-1}$). We identify an anomalous secondary injection mechanism driven primarily by quantum pressure, which can sustain turbulent fluctuations in such a system. By tuning the damping coefficient $γ$, we determine an optimal regime for energy transfer. While idealized, these findings illustrate how quantum turbulence with multiple scaling regimes can arise in pinned, rotating superfluids, and they suggest possible qualitative connections to vortex-mediated dynamics in neutron stars and other astrophysical superfluid systems.