An examination of spectral transfer of homogeneous anisotropic turbulence by means of closure and application in subgrid modeling

Noting that modeling flows for computer simulations of turbulence dynamics using finite element methods usually results in errors in the energy transfer between subgrid and grid scales, a quasi-normal closure model is developed to define a homogeneous turbulent field subjected to a mean shear. The energy transfers occur between large and small eddies and cannot be modeled by turbulent viscosity schemes. A field filter is defined which comprises energy transfers below the grid size, the interactions in the zone of small eddies, and the interactions in the subgrid between two elements in the small eddies. Finally, the relative spectra for exchanges between the large eddies and the scales of the subgrid are integrated.