Investigation of the effects of subgrid-scale turbulence on resolvable-scale statistics

The effects of the subgrid-scale (SGS) turbulence on the resolvable-scale statistics as well as the effects of SGS models on large-eddy simulation (LES) are studied. It is shown that the SGS turbulence evolves the resolvable-scale joint probability density function (JPDF) through the conditional means of the SGS stress, the SGS scalar flux, and their production rate, which must be reproduced by the SGS model for LES to predict correctly the one-point resolvable-scale statistics, a primary goal of LES. This necessary condition is used as the basis for studying SGS physics and for testing SGS models. Theoretical predictions, measurements data, and numerical simulation results are combined to investigate the effects of filter size, the dependence of the SGS turbulence on the flow dynamics, and SGS models performance using new a priori and a posteriori tests developed in this research. For inertial-range filter scales, LES statistics of the energyand flux-containing scales are generally considered to be insensitive to the SGS model employed. To examine this premise, the effects of the subgrid-scale (SGS) velocity, scalar, and SGS models on the resolvable-scale velocityscalar joint probability density function (JPDF) are studied. The mean SGS stress and SGS scalar flux production rate is predicted using Lumley’s assumption (Lumley 1967), which is consistent with Kolmogorov’s hypothesis. Analyses of these statistics using data obtained in a slightly heated turbulent jet show that the mean SGS stress, SGS scalar flux, and their production rates have filterscale dependencies consistent with predictions, suggesting that the SGS turbulence has diminishing influence on the lower-order resolvable-scale statistics for inertial-range filter scales and supporting the premise of LES at the level of lower-order statistics. The measured conditional SGS stress and SGS flux as well as the conditional production rates have a strong dependence on the resolvablescale velocity and scalar, indicating strong flow history effects, and decrease much slower than the predicted filter dependencies, indicating that the SGS turbulence has non-trivial effects on the highorder resolvable-scale statistics even for inertial-range filter scales. For energy-containing filter scales, previous studies have shown that LES results depend strongly on the SGS models. To study the effects of the SGS turbulence on the resolvable-scale velocity statistics for such filter scales, the SGS stress in the atmospheric surface layer is studied using measurement data (HATS 2000). Analysis of the conditional SGS stress and the conditional stress production rate conditional on the resolvable-scale velocity show that both buoyancy and iii shear play important roles in the physics of the SGS stress. Strong buoyancy and vertical shear associated with updrafts and positive streamwise velocity fluctuations cause conditional forward energy transfer and strong anisotropy in the conditional SGS stress. Downward returning flows associated with large convective eddies result in much less anisotropic SGS stress and conditional energy backscatter. Predictions of the conditional SGS stress and the conditional stress production rate predicted using several SGS models are compared with measurements. None of the models tested are able to predict correctly the trends of both statistics. The deficiencies of the SGS models that cause inaccurate LES statistics, such as the over-prediction of the mean shear and under-prediction of the vertical velocity skewness, are identified. To study the effects of the SGS turbulence on the resolvable-scale velocity-scalar statistics for energy-containing filter scales, the SGS scalar flux in the atmospheric surface layer is studied using field measurements data. The results show that the conditional scalar flux and its production rate depend on the resolvable-scale velocity and temperature fluctuations, suggesting that these conditional variables have strong influences on the resolvable-scale statistics. The dependencies are argued to be due to the effects of buoyancy and flow history. The results show that the conditional vertical scalar flux affects the conditional horizontal scalar flux production rate. However, the conditional horizontal scalar flux has no direct effect on the conditional vertical scalar production rate. Therefore, the correct modeling of the conditional vertical scalar flux components is crucial. Predictions of the conditional scalar flux and its production rate predicted using several SGS models are compared with measurements. The current SGS models have varying levels of performance in predicting different SGS flux components. As a results, the poor prediction of one SGS component often affects the prediction of the production rate of another SGS component, thereby resulting in errors in the LES statistics. Therefore, efforts to improve SGS models need to ensure that all the relevant SGS fluxes related to the LES statistics of interests or of importance to the intended applications are correct predicted. The present study shows that analysis of the conditional statistics can serve as an important guide in studying the SGS physics, identifying model deficiencies, and developing improved SGS models. To understand the model performance, a new a posteriori test is employed to study SGS model performance. Unlike traditional a posteriori tests of SGS models, which often compare LES profiles of various statistics with measurements, the new approach compares the conditional means of the LES-generated SGS stress and the conditional stress production rate conditional on the resolvable-scale velocity with measurements. The Smagorinsky model, the split model, and the Kosović model are tested. The LES results for convective atmospheric boundary layers show that iv the level of the anisotropy of the SGS stress represented in the Lumley triangle is under-predicted by both the Smagorinsky model and the Kosović model. The magnitudes of the conditional SGS stress and the conditional SGS stress production rate are generally under-predicted by both models as well. The trends of the conditional SGS stress and the conditional SGS stress production rate are generally better predicted by the Kosović model than that of the Smagorinsky model. The model strengths and deficiencies observed here were also identified in previous statistical a priori tests analyzing the conditional statistics. The remarkable consistency between the two types of tests suggests that statistical tests analyzing the conditional SGS stress and its production rate are capable of identifying specific model deficiencies and for evaluating SGS model performance in simulations.