Planar Variational Multi-Scale Modeling

The variational multi-scale (VMS) method for large-eddy simulation (LES) is a promising new approach that employs variational projection to achieve a priori scale separation in lieu of traditional spatial filtering. However, depending on the numerical method used, VMS may not be practicable in all spatial directions. We apply the VMS methodology to a numerical method that does not support explicit scale separation in the wall-normal direction for turbulent channel flow. Similar to the common LES practice of filtering only in the planes, variational projection is performed only in the planes and this strategy is found to be as successful as the full VMS method. Our findings make VMS available to a wide range of turbulence simulation tools.