Large eddy simulation of attached turbulent boundary layers becomes prohibitively expensive at high Reynolds numbers if one attempts to resolve the small, but dynamically important vertical structures in the near wall region. The Reynolds number scaling of the required number of grid points is nearly the same as for direct numerical simulation. To circumvent the severe near wall resolution requirement, LES is combined with a reduced order wall layer model. In this approach, LES is conducted on a relatively coarse grid designed to resolve the desired outer flow scales. The dynamic effects of the energy-containing eddies on the wall layer are determined from a wall model calculation, which provides to the outer flow LES a set of approximate boundary conditions, often in the form of a wall shear stresses.

In the first part of the presentation I will discuss the evolution of wall models from nearly four decades of research. While each method has had some success, none has demonstrated sufficient robustness for use in complex geometries at very high Reynolds numbers. An explanation for this difficulty will be provided. In the second part, we will argue that successful development of wall models must account for numerical and subgrid scale modeling errors. Since subgrid scale modeling and numerical errors cannot be known a priori and will be different for each simulation, we will use optimal flow control techniques to prescribe wall stresses for LES. Turbulent statistics in channel flow at high Reynolds numbers, obtained from an optimal control based wall model will be presented.