Data-based approach for time-correlated closures of turbulence models

TL;DR

This paper introduces a probabilistic, data-driven closure method for turbulence models using shell models and Gaussian Mixture Models, capturing intrinsic turbulence features with time correlation.

Contribution

It presents a novel closure approach based on shell models and probabilistic density functions, integrating machine learning tools for turbulence modeling.

Findings

Closure captures intrinsic probabilistic features of turbulence.

Framework allows integration of various machine learning techniques.

Time-correlated closures improve turbulence simulation accuracy.

Abstract

Developed turbulent motion of fluid still lacks an analytical description despite more than a century of active research. Nowadays phenomenological ideas are widely used in practical applications, such as small-scale closures for numerical simulations of turbulent flows. In the present work, we use a shell model of turbulence to construct a closure intended to have a solid theoretical background and to capture intrinsic probabilistic features of turbulence. Shell models of turbulence are dynamical deterministic systems used to model energy cascade and other key aspects of the Navier-Stokes such as intermittency. We rescale the variables of the Sabra model in a way which leads to hidden symmetries and universal distributions. We then use such fine distributions to write closures, i.e., missing expressions for some of the Sabra variables. Our closures rely on approximating probability density functions using a Gaussian Mixture Model, which makes them probabilistic by nature and allows us to write time-correlated closures. We also provide a framework where other Machine Learning tools can be employed with reduced black-box aspects.