Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box

TL;DR

This paper investigates whether ensemble eddy viscosity models over-diffuse turbulence solutions in a periodic box and proves that they do not, offering insights into turbulence modeling accuracy.

Contribution

It demonstrates that ensemble eddy viscosity models do not over-diffuse solutions in a periodic box, providing a theoretical validation for this approach.

Findings

Ensemble eddy viscosity models do not over-diffuse turbulence solutions in a periodic box.

The paper provides a mathematical proof supporting the accuracy of ensemble methods.

Results suggest ensemble approaches are reliable for turbulence simulation in periodic domains.

Abstract

Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not.