Physics of Fluids
Recent interest in the development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, provides the motivation for the present paper. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. This includes the frame-invariance properties of the filtered equations and the resulting residual stress. Causal time-domain filters, parametrized by a temporal filter width 0infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and both a priori and a posteriori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted for the model problem.
Original Publication Citation
Pruett, C.D., Gatski, T.B., Grosch, C.E., & Thacker, W.D. (2003). The temporally filtered Navier-Stokes equations: Properties of the residual stress. Physics of Fluids, 15(8), 2127-2140. doi: 10.1063/1.1582858
Pruett, C. D.; Gatski, T. B.; Grosch, Chester E.; and Thacker, W. D., "The Temporally Filtered Navier-Stokes Equations: Propertes of the Residual Stress" (2003). CCPO Publications. 185.