Turbulent pair dispersion with Stochastic Generative Diffusion Models

TL;DR

This paper introduces a diffusion model approach to generate synthetic pairs of turbulent Lagrangian trajectories, accurately capturing pair dispersion dynamics and key statistical properties, advancing data-driven turbulence modeling.

Contribution

The work extends diffusion models to jointly generate turbulent particle pairs, enabling a comprehensive data-driven representation of turbulent pair dispersion.

Findings

Diffusion models accurately reproduce particle-pair separation evolution.

The models capture deviations from Richardson's classical scaling law.

All key single-particle statistical properties are preserved.

Abstract

Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. We demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications.