Physics and modeling of small scale turbulence for large eddy simulation

Abstract

An important open question for Large Eddy Simulation (LES) of turbulent flow is whether the subgrid-scales (smaller than A) and the associated stresses can be described by universal models. This question is examined in terms of the subgrid dissipation rate, which represents the rate at which large-scale turbulent kinetic energy or scalar fluctuations are transferred to, or from, the unresolved scales. This variable is of central importance in LES. In order to ascertain the dependence of SGS dissipation upon large scales and the degree of universality of subgrid models, various high Reynolds number flows are studied. Hot-wire data (yielding, so far, 1-D surrogates only) in the turbulent plane wake (at Re _D = 8. 10⁴) shows that the phase-averaged surrogate SGS dissipation rate is very much affected by the presence of coherent (Kármán) vortices which occur at scales much larger than the filter scale, and that the effect persists down to very small scales. Strong effects of large-scale coherent structures are also observed in the atmospheric surface layer, as deduced from sonic anemometry data of the surrogate subgrid temperature variance dissipation. In comparing how different models reproduce the observed distribution of conditional SGS dissipation, the similarity model is found to capture the main features of the observed conditional SGS dissipation, while the Smagorinsky model gives less realistic distributions. The dynamic Smagorinsky model is able to reproduce the distribution, if the coefficient is obtained by means of conditional averaging

Thus, the experimental results (as well as numerical results by several other authors) show that there exists strong dependence of small scales upon the large ones. While the results weaken hopes for universality, they show that ‘learning’ from resolved scales about the local state of turbulence appears to improve the realism of the models. However, much depends on the details of how this learning process is implemented. For instance, in the localized dynamic models, problematic features such as unphysically high levels of intermittency can occur. This is demonstrated by detailed analysis of DNS of isotropic turbulence.