The subgrid-scale (SGS) potential temperature flux and stress in the atmospheric surface layer are studied using field measurement data. We analyse the mean values of the SGS temperature flux, the SGS temperature flux production rate, the SGS temperature variance production rate, the SGS stress and the SGS stress production rate conditional on both the resolvable-scale velocity and temperature, which must be reproduced by SGS models for large-eddy simulation to reproduce the one-point resolvable-scale velocity–temperature joint probability density function (JPDF). The results show that the conditional statistics generally depend on the resolvable-scale velocity and temperature fluctuations, indicating that these conditional variables have strong influences on the resolvable-scale statistics. The dependencies of the conditional SGS stress and the SGS stress production rate, which are partly due to the effects of flow history and buoyancy, suggest that model predictions of the SGS stress also affect the resolvable-scale temperature statistics. The results for the conditional flux and the conditional flux production rate vectors have similar trends. These conditional vectors are also well aligned. The positive temperature fluctuations associated with updrafts are found to have a qualitatively different influence on the conditional statistics than the negative temperature fluctuations associated with downdrafts. The conditional temperature flux and the temperature flux production rate predicted using several SGS models are compared with measurements in statistical a priori tests. The predictions using the nonlinear model are found to be closely related to the predictions using the Smagorinsky model. Several potential effects of the SGS model deficiencies on the resolvable-scale statistics, such as the overprediction of the vertical mean temperature gradient and the underprediction of the vertical temperature flux, are identified. The results suggest that efforts to improve the LES prediction of a resolvable-scale statistic must consider all the relevant SGS components identified using the JPDF equation and the surface layer dynamics. This study also provides impetus for further investigations of the JPDF equation, especially analytical studies on the relationship between the JPDF and the SGS terms that govern its evolution.
Conditional statistics of temperature fluctuations in turbulent convection
