Analysis of anisotropic subgrid-scale stress for coarse large-eddy simulation

TL;DR

This paper investigates the role of anisotropic subgrid-scale stress in large-eddy simulations of turbulent shear flows, revealing its significant contribution to coherent structure generation, especially at larger filter sizes, and highlighting the need for improved SGS models.

Contribution

It introduces a decomposition of SGS stress into isotropic and anisotropic parts and analyzes their distinct roles in turbulent shear flows at different filter sizes.

Findings

Anisotropic SGS stress has negligible energy transfer contribution.

Anisotropic stress significantly influences Reynolds stress components at large filter sizes.

Positive contribution of anisotropic stress aligns with streak spacing in near-wall turbulence.

Abstract

This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS stress in turbulent shear flows in addition to the energy transfer between grid-scale (GS or resolved scale) and SGS. One is the isotropic eddy-viscosity term, which contributes to energy transfer, and the other is the residual anisotropic term, which is separated from the energy transfer. We investigate the budget equation for GS Reynolds stress in turbulent channel flows accompanied by the SGS stress decomposition. In addition, we examine the medium and coarse filter length cases; the conventional eddy-viscosity models can fairly predict the mean velocity profile for the medium filter case and fails for the coarse filter case. The budget for GS turbulent kinetic energy shows that the anisotropic SGS stress has a negligible contribution to energy transfer. In contrast, the anisotropic stress has a large and non-dissipative contribution to the streamwise and spanwise components of GS Reynolds stress when the filter size is large. Even for the medium-size filter case, the anisotropic stress contributes positively to the budget for the spanwise GS Reynolds stress. Spectral analysis of the budget reveals that the positive contribution is prominent at a scale consistent with the spacing of streaks in the near-wall region. Therefore, we infer that anisotropic stress contributes to the generation mechanism of coherent structures. Predicting the positive contribution of the anisotropic stress to the budget is key to further improving SGS models.