Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation

A number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are evaluated: one based on the local equilibrium hypothesis (called local-dynamic models) and one based on the global equilibrium and steady state hypotheses (global-dynamic models). These local-dynamic (LD) and global-dynamic (GD) versions of MGM are found to be much more accurate than the constant coefficient MGM in neutral turbulent channel flow at friction Reynolds numbers of 180 and 590. The constant coefficient MGM and GD-MGM are also found to yield the correct asymptotic behaviour close to the wall, which indicates the suitability of coupling the MGM kernel with the GD procedure. For the SGS scalar flux vector, LD and GD versions of the MGM are evaluated along with LD and GD versions of the recently proposed Smagorinsky-gradient (SGM) and Vreman-gradient (VGM) models. Tests in neutral and stably stratified channel flow at friction Reynolds number of 180 and friction Richardson numbers of 0 and 18 reveal that all six dynamic SGS scalar flux vector models are able to reproduce first-order and second-order turbulent statistics accurately. The simulations help further establish the stability and accuracy of SGM and VGM, which have not been tested previously. None of the dynamic gradient-based SGS scalar flux vector models are found to yield the correct asymptotic behaviour, however, and this issue needs further investigation.