On Taylor-series expansions of residual stress

Although subgrid-scale models of similarity type are insufficiently dissipa tive for practical applications to large-eddy simulation, in recently publi shed a priori analyses, they perform remarkably well in the sense of correl ating highly against exact residual stresses. Here, Taylor-series expansion s of residual stress are exploited to explain the observed behavior and "su ccess" of similarity models. Specifically, the first few terms of the exact residual stress tau (kl) are obtained in (general) terms of the Taylor coe fficients of the grid filter. Also, by expansion of the test filter, a simi lar expression results for the resolved turbulent stress tensor L-kl in ter ms of the Taylor coefficients of both the grid and test filters. Comparison of the expansions for tau (kl) and L-kl yields the grid- and test-filter d ependent value of the constant c(L) in the scale-similarity model of Liu [J . Fluid Mech. 275, 83 (1994)]. Until recently, little attention has been gi ven to issues related to the convergence of such expansions. To this end, w e re-express the convergence criterion of Vasilyev [J. Comput. Phys. 146, 8 2 (1998)] in terms of the transfer function and the cutoff wave number of t he filter. As a rule of thumb, the less dissipative the filter (e.g., the h igher the cutoff), the faster the rate of convergence. (C) 2001 American In stitute of Physics.