Turbulence Scaling from Deep Learning Diffusion Generative Models
This work addresses the problem of modeling complex turbulent flows for researchers in fluid dynamics, but it is incremental as it applies an existing generative method to a new domain.
The authors tackled the challenge of understanding turbulent fluid flows by using a diffusion-based generative model to learn and generate turbulent vorticity profiles, and found that the generated profiles' scaling exponents matched the expected Kolmogorov scaling, confirming the model's ability to capture real-world turbulence features.
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. This agreement with established turbulence characteristics provides strong evidence of the model's capability to capture essential features of real-world turbulence.