We demonstrate the feasibility of a closure model for large-scale eddies in the energy-containing range of turbulence. To this end, we construct a data-driven closure model for the largest eddies in turbulence driven by the steady Taylor-Green force in a periodic cube, and thoroughly evaluate its stability and accuracy. A recurrent neural network is employed to autoregressively predict the temporal evolution of low-wave-number components of the Fourier coefficients of vorticity with a prediction interval $\mathrm{\Delta }{t}_{\mathrm{p}}$. The key factors for successful modeling are not only spatial low-pass filtering to construct the closure model, but also preprocessing the training data with a temporal low-pass filter. More concretely, an appropriate cutoff frequency, which is inversely proportional to $\mathrm{\Delta }{t}_{\mathrm{p}}$, is needed for stable and accurate reproduction of the dynamics and statistics of the largest eddies. Without this preprocessing, the model exhibits steady or periodic behavior and fails to reproduce the chaotic dynamics of the largest eddies.

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• Turbulence
• Turbulence modeling
• Chaotic systems
• Machine learning