Numerical proof of shell model turbulence closure

We focus on the development of turbulence subgrid closure models that, employed in an LES approach, exhibit intermittent effects and energy cascade dynamics that are statistically indistinguishable from those of the fully resolved turbulent system. Due to the massive amount of data needed to reach converged statistics of high order statistical moments, we consider the setting of Shell Models of Turbulence, reduced dynamical systems of Ordinary Differential Equations that have been shown to rather faithfully mimic the phenomenology of the energy cascade of Homogeneous Isotropic Turbulence in Fourier space

Our method employs a novel custom-made Deep Learning architecture comprising a classical 4th order Runge-Kutta integration scheme for the large scales of turbulence augmented with a Recurrent Artificial Neural Network, modelling the subgrid closure term. Using this approach we are able to reproduce, within statistical error bars, the intermittent behavior found in the full model, obtaining the correct scaling laws for Eulerian and Lagrangian structure functions and outperforming classical physics based methods.

This work demonstrates the capability of Machine Learning to capture complex multiscale dynamics and reproduce complex multi-scale and multi-time non-gaussian behaviors, opening up the possibility to tackle turbulence modelling in Navier-Stokes Equations.