Scaling analysis on filtered near wall turbulence

Large Eddy Simulations (LES) directly represent larger scale turbulent motions and model the effects of small scale motions. However in the near wall region the large dynamically important eddies scale in viscous wall units, which makes resolving them in a high Reynolds number LES very expensive. This motivates the use of wall-modeled LES, in which these near-wall eddies are modeled. To aid in the development of new wall models, we pursue an asymptotic analysis of the filtered Navier-Stokes equations, in the limit in which the horizontal filter scale is large compared to the thickness of the wall layer. It will be shown that in this limit the filtered velocities $\bar{u}$ and subgrid stresses $\bar{\tau}$ in the near-wall layer are determined to zeroth order by filtered velocities at the boundary of the wall layer. Further the asymptotics suggest that there is a scaled universal velocity profile $f$ and subgrid stress profile $g$ in the near-wall region. The validity of this result will be tested and the profiles $f$ and $g$ will be evaluated through analysis of DNS data from channel flow at $Re_{\tau}=5200$.