Description
Quantum turbulence in high-energy-density plasmas can significantly alter the transport of energy during inertial confinement fusion and astrophysical processes. We develop a theoretical framework, based on classical, weakly compressible turbulence analysis for homogeneous isotropic quantum turbulence using the inviscid, unmagnetized Poisson Quantum Hydrodynamic (QHD) equations with zero electric field. Ensemble averaging of the turbulent flow around the mean velocities allow us to obtain the transport of turbulent kinetic energy. Wave-wave interactions in Fourier space allow for analysis of the dynamics of quantum turbulence in spectral space. Analytical predictions of turbulent quantities and energy spectrum are validated through computational
means, via the lattice Boltzmann method (LBM) with canonical turbulence benchmarks serving to ensure numerical accuracy. We adapt classical LBM to simulate quantum turbulence. This approach provides insight into how quantum contributions modify classical turbulent spectra and lays the foundation for future studies that incorporate viscosity, electromagnetic forcing, and experimental validation in fusion-relevant conditions.