The objective of the study is to investigate the capability of PANS (Partially Averaged Navier-Stokes Simulation) model over a wide range of Reynolds numbers and flow physics. In this regard, numerical simulations of turbulent flow past a circular cylinder are performed at ReD 140,000 and ReD 3900 using the PANS model. The high Reynolds number PANS results are compared with experimental results from Cantwell and Coles, Large Eddy Simulation results from Breuer, and Detached Eddy Simulation results from Travin et al. Low Reynolds number PANS results are compared with experimental results from Ong and Wallace and Large Eddy Simulation results from Breuer. The effects of the various PANS parameters (fk, fε, σku, σεu) on the ability to capture turbulence physics at various Reynolds numbers are studied. It is confirmed, as previously predicted from theoretical considerations that: (i) for high Reynolds number flow fε = 1 and σku = σk × fk2 / fε are most appropriate; and (ii) for low Reynolds number flow fε = fk and σku = σk are most suitable. These choices for the parameters stem from the fact that there is no clear separation of scales between the energy scales and the dissipation scales at low Reynolds number unlike in the high Reynolds number where there is a clear separation of scales between the energy containing scales and the dissipation scales. Also, in both cases it is found that decreasing fk leads to improved accuracy in predicting the flow statistics.

Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.

Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.