Conditional subgrid force and dissipation in locally isotropic and rapidly strained turbulence

Modeling of the small scales of turbulence for large eddy simulation (LES) requires a sound understanding of the relationships between large and small scales of motion. Conditional averaging allows us to isolate the effects of specific large-scale flow features in a statistically meaningful fashion. We study how regions of large-scale straining, rotation, and energy cascade rate affect SGS quantities of direct dynamical relevance for LES, namely the subgrid-scale (SGS) force (the divergence of the SGS stress tensor), and the SGS dissipation rate. Conditional averages are measured from experimental data in two flows: (i) the far field of a turbulent jet, and (ii) initially near-isotropic turbulence undergoing rapid axisymmetric expansion. These data are representative of near-equilibrium, locally isotropic turbulence, and of a nonisotropic, nonequilibrium turbulent flow, respectively. The separation between large and small scales is performed with a spatially compact box filter. Results for the locally isotropic data show that the SGS force surrounding points of large strain-rate magnitude is nearly radial. Due to the divergence-free condition of the velocity field, such SGS force can only affect the resolved pressure field. Being directed outwards, the SGS force decreases the resolved pressure in regions of high strain-rate magnitude. Similar results are obtained in regions of large resolved dissipation, defined as the energy flux into the smallest resolved band of scales. No effect of the resolved vorticity is found. In the rapidly distorted flow, the SGS force in regions of large positive resolved dissipation is found to affect both the resolved pressure (again decreasing it) and the resolved velocity (the SGS motions oppose the mean deformation). Regions of large negative resolved dissipation (backscatter) exhibit the opposite effect, acting in such a way as to favor the mean deformation. The mixed model is shown to provide better predictions of conditional SGS dissipation than the Smagorinksy or the similarity models alone. However, observed discrepancies in the conditional SGS force imply the need for further model improvements.