Optimized dynamic similarity models to predict SGS backscatter in 2D decaying turbulence

Large eddy simulation (LES) of two-dimensional (2D) turbulence is often used in the geostrophic flows. However, some basic dynamics underlying traditional SGS models are absent in 2D turbulence, e.g. the vortex stretching. Hence, this research proposes an optimized dynamic similarity model (DSM) for the SGS stress, which is constructed through the dynamic procedure based on the Germano identity. In addition, a modification is made to the dynamic mixed model (DMM) for the sake of realizability condition. The optimized DSM is justified in comparison with the DMM, through the a priori and a posteriori verifications, in the context of the 2D decaying turbulence with turbulent Reynolds number of $Re=3.7\times 10^4$ and turbulent Mach number of $M_t=0.1$. Special attention is paid to the consistency of the verification procedure, so that the filtering operations used in the direct numerical simulation (DNS) and LES are optimally equivalent. The SGS transport phenomena, especially the SGS backscatter, predicted by these two models are studied in detail. In addition, the optimized DSM and the DMM are extended for the modified SGS transport vectors of passive scalars to show their capability in calculating 2D turbulent mixing. The numerical results show the optimized DSM provides larger correlation coefficient, better locality, and stronger SGS backscsatter than the DMM does, and therefore it is more suitable for the LES of 2D turbulence.