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Optimal subgrid scheme for shell models of turbulence.

Luca Biferale¹, Alexei A Mailybaev², Giorgio Parisi³

¹Department of Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Rome, Italy.

Physical Review. E

|May 17, 2017

Summary

This study introduces an optimal subgrid closure for turbulence shell models, improving large-scale dynamics prediction. Approximations show good performance but reveal scale-dependent discrepancies, suggesting potential instabilities in turbulence modeling.

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Area of Science:

Turbulence theory
Computational fluid dynamics
Statistical physics

Background:

Turbulence modeling requires accurate subgrid-scale (SGS) closures.
Shell models are simplified representations of three-dimensional Navier-Stokes turbulence.
Kolmogorov's hypotheses provide foundational principles for turbulence scaling.

Purpose of the Study:

To develop a theoretical framework for an optimal SGS closure in turbulence shell models.
To investigate systematic approximations of this optimal closure.
To assess the performance of low-order closures in reproducing turbulence dynamics.

Main Methods:

Developed a closure based on short-range correlations of shell multipliers, inspired by Kolmogorov's third hypothesis.
Proposed systematic approximations by varying correlation degrees across scales.
Conducted numerical simulations to evaluate model performance and scaling properties.

Main Results:

Low-order closures accurately reproduce large-scale dynamics and anomalous scaling.
Small, systematic discrepancies were observed near the subgrid threshold.
These discrepancies did not diminish with higher-order approximations, suggesting scale-dependent issues.

Conclusions:

The proposed closure framework is effective for turbulence shell models.
Discrepancies near the subgrid threshold may indicate underlying structural instabilities.
Findings offer insights for improving large eddy simulations of Navier-Stokes equations.