Forecasting small-scale dynamics of fluid turbulence using deep neural networks

Area of Science:

• Fluid Dynamics
• Computational Physics
• Machine Learning

Background:

• Turbulent flows exhibit complex, multi-scale dynamics, making high Reynolds number simulations computationally prohibitive.
• Accurately modeling small-scale turbulent motions is crucial due to their universal characteristics and high computational cost.
• Traditional modeling approaches face challenges in capturing the full range of small-scale turbulence phenomena.

Purpose of the Study:

• To develop a physics-informed deep learning framework for modeling and predicting small-scale turbulence dynamics.
• To create functional closures for pressure Hessian and viscous Laplacian terms using deep neural networks.
• To incorporate Reynolds number dependence and physical constraints into the deep learning model for improved accuracy.

Main Methods:

• Utilized physics-informed deep learning to model the velocity gradient tensor in turbulent flows.
• Developed deep neural networks to learn functional closures for pressure Hessian and viscous Laplacian.
• Trained and validated the model using a large direct numerical simulation database across two orders of magnitude in Reynolds number.

Main Results:

• The deep learning model successfully captures and predicts small-scale turbulence dynamics.
• The model accurately predicts velocity gradient statistics at both seen and unseen Reynolds numbers.
• Demonstrated the model's ability to account for small-scale intermittency and Reynolds number dependence.

Conclusions:

• Physics-informed deep learning offers a viable and powerful alternative to traditional methods for turbulence modeling.
• The developed framework effectively captures essential small-scale features of turbulence.
• This approach shows significant promise for advancing the simulation and understanding of high Reynolds number flows.