LES of Turbulent Channel Flow at Large $Re_{\tau}$

Large-eddy simulation (LES) of turbulent channel flow will be discussed. A special near-wall, subgrid-scale (SGS) model is developed based on wall-normal averaging of the streamwise momentum equation and local inner scaling combined with an extended form of the stretched-vortex, subgrid-scale (SGS) model. The latter incorporates production of Reynolds shear stress produced by the winding of streamwise momentum by near-wall, attached, SGS vortices. This then allows calculation of an instantaneous slip velocity that is then used as a ``virtual-wall'' boundary condition for the LES within the log region. A K\'arm\'an-like constant is calculated dynamically as part of the LES. With this closure, LES of turbulent channel flow will be presented for $Re_{\tau}$ in the range $2\,\times 10^3$ -- $2\,\times 10^7$.