  A novel approach to wall modeling for the incompressible Navier-Stokes
equations including flows of moderate and large Reynolds numbers is presented.
The basic idea is that a problem-tailored function space allows prediction of
turbulent boundary layer gradients with very coarse meshes. The proposed
function space consists of a standard polynomial function space plus an
enrichment, which is constructed using Spalding's law-of-the-wall. The
enrichment function is not enforced but "allowed" in a consistent way and the
overall methodology is much more general and also enables other enrichment
functions. The proposed method is closely related to detached-eddy simulation
as near-wall turbulence is modeled statistically and large eddies are resolved
in the bulk flow. Interpreted in terms of a three-scale separation within the
variational multiscale method, the standard scale resolves large eddies and the
enrichment scale represents boundary layer turbulence in an averaged sense. The
potential of the scheme is shown applying it to turbulent channel flow of
friction Reynolds numbers from $Re_{\tau}=590$ and up to $5,000$, flow over
periodic constrictions at the Reynolds numbers $Re_H=10,595$ and $19,000$ as
well as backward-facing step flow at $Re_h=5,000$, all with extremely coarse
meshes. Excellent agreement with experimental and DNS data is observed with the
first grid point located at up to $y_1^+=500$ and especially under adverse
pressure gradients as well as in separated flows.
