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This study models small-scale turbulence using machine learning on a Shell model. The novel approach improves reduced models, offering probabilistic and cutoff-independent closures for turbulent flow simulations.

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Area of Science:

  • Fluid Dynamics
  • Computational Physics
  • Machine Learning Applications

Background:

  • Turbulent flow modeling is complex, with challenges in analytically describing small scales of motion.
  • Accurate modeling of small scales is vital for efficient numerical simulations in industrial applications.
  • Shell models offer a computationally tractable approach to simulating turbulence, preserving key Navier-Stokes properties like energy cascade and intermittency.

Purpose of the Study:

  • To develop closures for the Sabra Shell model to accurately represent small scales of turbulent motion.
  • To utilize machine learning techniques for data-driven modeling of turbulence dynamics.
  • To create reduced models of turbulence that are computationally efficient yet statistically accurate.

Main Methods:

  • Applied scaling relations to Sabra Shell model data to recover hidden symmetries and universal statistics.
  • Employed variational auto-encoder and sparse identification of non-linear dynamics (SINDy) on rescaled data.
  • Generated new data instances to close reduced models, resolving only larger scales of motion.

Main Results:

  • Developed probabilistic and cutoff-independent closures for the Sabra Shell model.
  • Reduced models incorporating machine learning closures showed improved statistical accuracy compared to previous methods.
  • Performance of reduced models was evaluated against fully resolved Sabra simulations.

Conclusions:

  • Machine learning closures effectively model small-scale turbulence dynamics within a Shell model framework.
  • The proposed method offers a promising avenue for enhancing the efficiency and accuracy of turbulent flow simulations.
  • The developed closures demonstrate robustness, being both probabilistic and independent of the cutoff scale.