Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence

Abstract

Using results of direct numerical simulations of isotropic turbulence the subgrid-scale energy transfer in the physical space is calculated exactly employing a spectral decomposition of the velocity field into large (resolved) and small (unresolved) scales. Comparisons with large-scale quantities reveal large qualitative correlations between regions of subgrid transfer and the boundaries of regions of large vorticity production. This suggests a novel analysis of the nonlinear term, where it is decomposed into four components determined by four combinations of the resolved and unresolved velocity and vorticity fields. It is found that there is a 90% vector-correlation between the subgrid transfer and the component of the full transfer associated with the resolved velocity and unresolved vorticity, but that 90% of the total subgrid energy production is determined by the component associated with the unresolved velocity and resolved vorticity. These results suggest subgrid-scale models that have higher correlation values with the exact subgrid scale terms than a number of other physical quantities that are traditionally considered to govern the dynamics of the large scales of turbulence. The distinguishing feature of the new models is that they emphasize the nonlinear dynamics of the smallest resolved scales in the modeling procedures.

Mixed nonlinear LES for DES suitable flows

“…There are many differences between the DNS analysis, the parameterization tests using decaying, isotropic turbulence, and the channel flow LES. These are that a wavenumber cut-off filter was used in the DNS analysis 17 instead of a Helmholtz filter as we now believe is correct, the Leray terms have never been tested in DNS analysis, and a Smagorinsky eddy viscosity was used for the decaying, isotropic LES tests instead of the k − l eddy viscosity. New DNS analysis is planned to determine the effect of these differences and the decaying, isotropic LES tests will be repeated with a k − l eddy viscosity.…”

“…In the analysis of DNS, 17 it was found that in addition to backscatter generated by subgrid terms, there was a second term that was dissipative and was similar to the prediction of an eddy viscosity model. It has been claimed that the regularization models, without eddy viscosities, are an alternative method of LES.…”

“…The study most relevant to the present work 17 showed that the full subgrid transfer terms could be divided into two primary components. A component that looks like a traditional eddy viscosity and another term that represents the convection of the subgrid vorticity by the resolved scales and contains all the backscatter.…”

“…One model adds −u× − → ω , as suggested by the DNS analysis. 17 This formulation conserves circulation and is equivalent to the recently introduced Lagrangian averaged Navier-Stokes equations or α-model. 25 Another model will be based upon (u · ∇)u , which was originally introduced in the classic mathematical study of regularization by Leray. 26 The third filtered model is (u · ∇)u + (u · ∇)u, which is the nonlinearity suggested by Clark et al…”

“…To understand the origin of backscatter, systematic analyses of the energy transfer between the large and small scales in direct numerical simulations and experiments [15][16][17] have been done. The study most relevant to the present work 17 showed that the full subgrid transfer terms could be divided into two primary components.…”