Turbulence Scaling from Deep Learning Diffusion Generative Models
Tim Whittaker Romuald A. Janik Yaron Oz
Complex spatial and temporal structures are inherent characteristics of
turbulent fluid flows and comprehending them poses a major challenge. This
comprehesion necessitates an understanding of the space of turbulent fluid flow
configurations. We employ a diffusion-based generative model to learn the
distribution of turbulent vorticity profiles and generate snapshots of
turbulent solutions to the incompressible Navier-Stokes equations. We consider
the inverse cascade in two spatial dimensions and generate diverse turbulent
solutions that differ from those in the training dataset. We analyze the
statistical scaling properties of the new turbulent profiles, calculate their
structure functions, energy power spectrum, velocity probability distribution
function and moments of local energy dissipation. All the learnt scaling
exponents are consistent with the expected Kolmogorov scaling and have lower
errors than the training ones. This agreement with established turbulence
characteristics provides strong evidence of the model's capability to capture
essential features of real-world turbulence.