Wall-Bounded Turbulence

We explore the treatment of near-wall turbulence in coarse grained representa- tions of wall-bounded turbulence. Such representations are complicated by the fact that at high Reynolds number the near-wall effects occur in an asymptotically thin layer. Because of this, many near-wall models are posed as effective boundary conditions, essentially eliminating the thin wall layer which is too thin to resolve. This is commonly referred to as wall-modeled large eddy simulation, and the viability of this approach is supported by the weakness of the interaction between the near-wall turbulence and that further away. Such models are generally in- formed by known characteristics of near-wall turbulence, such as the log-layer in the mean velocity and the so-called law-of-the-wall. In this chapter, we consider such coarse grained near-wall models and the approximations implicit in their formulation from the perspective of thin-layer asymptotics.