Assessment of SGS Models for Large Eddy Simulation (LES) of a Stratified Taylor–Green Vortex

Abstract

Eddy viscosity-based and regularization-based subgrid-scale (SGS) models are quantitatively assessed for large eddy simulations (LES) of stratified Taylor–Green vortex (TGV). LES calculations using the dynamic Smagorinsky, Leray- $$\alpha$$ , LANS- $$\alpha$$ and Clark- $$\alpha$$ models are conducted using a pseudo-spectral formulation on a $$128^{3}$$ grid and using $$\alpha =\frac{1}{160}$$ (for all the regularization models) for Froude number, $$Fr_0=\frac{{\mathcal {U}}}{{{\mathcal {N}}}{{\mathcal {L}}}}=1$$ , and Reynolds number, $$Re_{0}= \frac{\mathcal {U L} }{\nu }=1600$$ . Results are compared in detail with in-house direct numerical simulation (DNS) calculations. Validation of the formulation is carried out through grid-dependent studies using grids of $$64^3$$ , $$128^3$$ and $$256^3$$ , $$\alpha$$ (regularization parameter)-dependent studies using $$\alpha$$ values of $$\frac{1}{40}, \frac{1}{80}, \frac{1}{160}$$ and $$\frac{1}{320}$$ , and comparisons with previously published results Remmler and Hickel, 2012, of the same problem. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), Q-criteria based vortical structures, potential & total energy spectra, and horizontal & vertical energy fluxes in the respective directions, are analyzed to understand the capability of the various LES models in predicting the development of stratified turbulence. Results showed that all the SGS model predictions were very similar to each other with Smagorinsky and Leray displaying the lowest and highest errors, respectively, in comparison to DNS. The effect of $$Fr_0$$ was also studied through additional LES calculations at $$Fr_0=0.5$$ and 0.16, again using the dynamic Smagorinsky and regularization models and comparing various parameters including tke, tpe and energy spectra to DNS. Decay rates of tke and tpe decreased and turbulence was significantly suppressed with decrease in $$Fr_0$$ . At these lower $$Fr_0$$ , all the SGS model predictions were almost identical to each other and compared extremely well with the DNS results.