A dynamic subfilter-scale model for plane parallel flows

We present a dynamic model of the subfiltered scales in plane parallel geom etry using a generalized, stochastic rapid distortion theory (RDT). This ne w model provides expressions for the turbulent Reynolds subfilter-scale str esses via estimates of the subfilter velocities rather than velocity correl ations. Subfilter-scale velocities are computed using an auxiliary equation which is derived from the Navier-Stokes equations using a simple model of the subfilter energy transfers. It takes the shape of a RDT equation for th e subfilter velocities, with a stochastic forcing. An analytical test of ou r model is provided by assuming delta-correlation in time for the supergrid energy transfers. It leads to expressions for the Reynolds stresses as a f unction of the mean flow gradient in the plane parallel geometry and can be used to derive mean equilibrium profiles both in the near-wall and core re gions. In the near-wall region we derive a general expression for the veloc ity profile which is linear in the viscous layer and logarithmic outside. T his expression involves two physical parameters: the von Karman constant an d the size of the viscous layer (which can be computed via a numerical impl ementation of our model). Fits of experimental profiles using our general f ormula provides reasonable values of these parameters (kappa =0.4 to kappa =0.45, the size of the viscous layer is about 15 wall units). In the core r egion, we find that the shape of the profile depends on the geometry of the flow; it ranges from algebraic in channel flow, to exponential in the bulk of boundary layers, and linear in plane Couette flow. This classification is consistent with Oberlack's system, which is based on symmetry arguments. Fits of boundary layer flows or channel flows at different Reynolds number over the whole flow region are performed using our results, and are found to be in very good agreement with available data. (C) 2001 American Institu te of Physics.