Multiscale properties of Large Eddy Simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

TL;DR

This paper investigates the multiscale correlations between resolved velocity fields and subgrid-scale stresses in large eddy simulations, comparing theoretical predictions with numerical data to evaluate and improve SGS modeling.

Contribution

It derives exact LES equations for velocity structure functions and tests multifractal predictions against high-resolution LES and DNS data, highlighting areas for SGS model improvement.

Findings

LES data aligns well with filtered DNS and multifractal theory

Discrepancies found in subleading correlation terms

Room for SGS model enhancement to extend inertial range

Abstract

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier-Stokes equations (NSE), we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the sub-grid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the subleading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.