A Predictive Near-Wall Model for Large Eddy Simulations

Large eddy simulations 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 are on the order of viscous scales, which makes resolving them very expensive. It is therefore desirable to formulate an approach where the near-wall region is modeled, leading to the so-called wall-modeled LES.

Spectral analysis of the DNS data indicates that thin-layer asymptotics is a promising approach to model the interactions between the near-wall layer and the outer flow. For this approach an asymptotic analysis of the filtered Navier-Stokes equations is pursued in the limit in which the horizontal filter scale is large compared to the thickness of the wall layer. It is shown in
this limit that the filtered velocities 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 $f$ in the near-wall region. The profile $f$ is evaluated through analysis of DNS data from channel flow at $Re_{\tau}=5200$. The
resulting profile $f$ is used to formulate a predictive near-wall model. We present preliminary results from a coarse LES using this wall model.