Subgrid-scale stress and its production rate: Conditions for the resolvable-scale velocity probability density function

Abstract

The effects of the subgrid-scale (SGS) turbulence and SGS models on the one-point joint probability density function (JPDF) of resolvable-scale velocity are studied using its transport equation. It is shown that the SGS stress evolves the JPDF through the conditional means of the SGS stress and its production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model in order for large-eddy simulation (LES) to reproduce the JPDF. Measurements are conducted in an axisymmetric turbulent jet using an array consisting of three X-wire probes to obtain filtered variables for analysing the conditional means. Data for three filter scales show that both the conditional SGS stress and the conditional SGS stress production rate depend strongly on the resolvable-scale velocity. While the magnitude of the conditional SGS stress decreases with the filter scale, that of the conditional SGS stress production does not, suggesting persistent effects on the resolvable-scale velocity JPDF. Therefore, the SGS model must be able to reproduce the conditional SGS stress production even for inertial-range filter scales. The conditional production of SGS normal stress (energy transfer) has some negative values, indicating conditional backscatter of SGS energy. This provides direct evidence that for LES to reproduce the JPDF it is essential for the SGS models to predict (conditional) backscatter. The Smagorinsky model is capable of predicting the qualitative features of the conditional SGS stress but not those of the conditional SGS stress production, especially the conditional backscatter. The present study links the resolvable-scale statistics to the dynamics of the SGS stress, providing impetus for further study of the SGS dynamics.