The scales associated with turbulent motions in the boundary layer range from the Kolmogorov dissipation scale (on the order of a millimeter) to the boundary layer depth (on the order of a kilometer). The largest eddies are responsible for the turbulent transport of scalars and momentum whereas the smallest ones are mainly dissipative. Large-Eddy Simulations (LES) consists of explicitly resolving all scales of turbulent transport larger than the grid scale (on the order of tens of meters in the ABL), while the smallest (less energetic) scales are parameterized using subgrid-scale (SGS) models.

The filtered LES equations are

• for momemtum:
  

• for heat:
  

where the tilde denotes filtering at a particular scale and the subgrid-scale stress and flux read:

As mentioned previously, these SGS quantities need to be parameterized and our research is devoted to develop models for such quantities, in particular:

• Eddy-viscosity/eddy-diffusion type models (Smagorinsky, Dynamic, Scale-Dependent Dynamic)

• Similarity, Nonlinear and Mixed models

• Fractal/Multifractal models

See our publications.