A Numerical Proof of Shell Model Turbulence Closure

TL;DR

This paper introduces a deep learning-based turbulence closure model using recurrent neural networks that accurately reproduces key statistical features of shell model turbulence, offering a promising approach for complex 3D turbulence modeling.

Contribution

It presents a novel neural network closure model that quantitatively captures statistical properties of shell model turbulence, advancing turbulence modeling techniques.

Findings

Reproduces Eulerian and Lagrangian structure functions within statistical errors.

Accurately captures intermittency and energy cascade statistics.

Demonstrates potential for application to 3D Navier-Stokes turbulence.

Abstract

The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure, based on deep recurrent neural networks, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, we employ shell models of turbulence. Our results encourage the development of similar approaches for 3D Navier-Stokes turbulence.