Partially-averaged Navier-Stokes model for turbulence: A Reynolds-averaged Navier-Stokes to direct numerical simulation bridging method

A turbulence bridging method purported for any filter-width or scale resolution-fully averaged to completely resolved-is developed. The method is given the name partially averaged Navier-Stokes (PANS) method. In PANS, the model filter width (extent of,partial averaging) is controlled through two parameters: the unresolved-to-total ratios of kinetic energy (f(k)) and dissipation (f(epsilon)). The PANS closure model is derived formally from the Reynolds-averaged Navier-Stokes (RANS) model equations by addressing the following question: if RAINS represents the closure for fully averaged statistics, what is the corresponding closure for partially averaged statistics.? The PANS equations vary smoothly from RANS equations to Navier-Stokes (direct numerical simulation) equations, depending oil the values of the filter-width control parameters. Preliminary results are very encouraging.