Synthetic Lagrangian turbulence by generative diffusion models.

Area of Science:

• Fluid Dynamics
• Turbulence Physics
• Machine Learning Applications

Background:

• Lagrangian turbulence is crucial for understanding dispersion and mixing across various scientific fields.
• Existing models fail to accurately capture statistical and topological features of particle trajectories in turbulence.

Purpose of the Study:

• To develop a machine learning model capable of generating realistic single-particle trajectories in high-Reynolds-number turbulence.
• To bypass the need for computationally expensive direct numerical simulations or experiments for Lagrangian data.

Main Methods:

• Utilized a state-of-the-art diffusion model, a type of machine learning approach.
• Applied the model to generate synthetic single-particle trajectories in 3D turbulence at high Reynolds numbers.

Main Results:

• The model successfully reproduces key statistical benchmarks, including fat-tail distributions and anomalous power laws.
• It accurately captures intermittency near the dissipative scale and shows strong generalizability for extreme events.
• Minor deviations were noted in acceleration and flatness statistics below the dissipative scale.

Conclusions:

• The proposed machine learning approach effectively generates high-quality synthetic Lagrangian turbulence data.
• This method overcomes limitations of traditional simulations and experiments, enabling new avenues for research.
• The generated datasets can be used for pretraining downstream applications in Lagrangian turbulence studies.