AI-based separation of turbulence from coherent background flows in decaying hydrodynamic turbulence

Abstract

Separating turbulent fluctuations from coherent large-scale background flows is a longstanding challenge in the analysis of numerical simulations and astronomical observations. Traditional approaches commonly rely on decomposition-based techniques such as Fourier or wavelet filtering, which assume that a meaningful separation can be achieved through scale selection. In realistic flows, however, coherent motions and turbulence often overlap across a broad range of scales and interact nonlinearly, making a unique separation inherently ambiguous. In this work, we investigate the robustness of an AI-based turbulence-background separation approach using two-dimensional incompressible Navier-Stokes simulations of decaying hydrodynamic turbulence. The simulations are initialized with a coherent background flow and divergence-free turbulent perturbations with a Kolmogorov-like spectrum and evolve without external forcing, providing a controlled physical testbed. A neural network trained exclusively on static synthetic images is applied to simulation snapshots at different evolutionary stages. The model recovers turbulent fluctuations during early and intermediate stages when partial scale separation is present. At later stages, where nonlinear interactions increasingly mix coherent and turbulent structures, the separation becomes less distinct; nevertheless, the recovered fields remain visually and spectrally consistent with the expected turbulent behavior. Quantitative comparisons with a Fourier filtering baseline show that the AI-based approach achieves comparable reconstruction accuracy while not requiring an explicit spectral cutoff scale. These results suggest that AI models trained on static data can provide a flexible diagnostic tool for turbulence-background separation in time-evolving flows, with potential applications to astrophysical datasets.