Synchronizing subgrid scale models of turbulence to data.

Large Eddy Simulations of turbulent flows are powerful tools used in many engineering and geophysical settings. Choosing the right value of the free parameters for their subgrid scale models is a crucial task for which the current methods present several shortcomings. Using a technique called nudging we show that Large Eddy Simulations can synchronize to data coming from a high-resolution direct numerical simulation of homogeneous and isotropic turbulence. Furthermore, we found that the degree of synchronization is dependent on the value of the parameters of the subgrid scale models utilized, suggesting that nudging can be used as a way to select the best parameters for a model. For example, we show that for the Smagorinsky model synchronization is optimal when its constant takes the usual value of $0.16$. Analyzing synchronization dynamics puts the focus on reconstructing trajectories in phase space, contrary to traditional a posteriori tests of Large Eddy Simulations where the statistics of the flows are compared. These results open up the possibility of utilizing non-statistical analysis in a posteriori tests of Large Eddy Simulations.