The t-Model as a Large Eddy Simulation Model for the Navier-Stokes Equations

The recently developed optimal prediction-based t-model [O. Hald and P. Stinis, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 6527–6532] is quantitatively assessed as a reduced-order model or large eddy simulation (LES) model for the Navier–Stokes (NS) equations. The t-model is based on the idea that the organization of a fluid flow in vortices leads to “long memory” effects; i.e., the motion of a vortex at one scale is influenced by the past history of the motion of vortices in other scales. LES predictions using the t-model are compared to the classic nondynamic Smagorinsky model for decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor–Green vortex (TGV) problems with periodic boundary conditions. Comparisons are made to laboratory measurements and direct numerical simulation (DNS) depending on the case. The Smagorinsky model shows good agreement with measurements and DNS. Regarding the t-model, while excellent comparisons are obtained at low-$Re$, for the high-$Re$ DHT, predi...