  The main objective of this work is to develop a unified framework that can be
used as a lens to quantitatively assess and augment a wide range of
coarse-grained models of turbulence, viz. large eddy simulations (LES), hybrid
Reynolds-averaged/LES methods and wall-modeled (WM)LES. Taking a turbulent
channel flow as an example, optimality is assessed in the wall-resolved limit,
the hybrid RANS/LES limit and the WMLES limit, via projections at different
resolutions suitable for these approaches. These optimal a priori estimates are
shown to have similar characteristics to existing a posteriori solutions
reported in the literature. Consistent accuracy metrics are developed for
scale-resolving methods using the optimal solution as a reference, and
evaluations are performed. We further characterize the slip velocity in WMLES
in terms of the near-wall under-resolution and develop a universal scaling
relationship. Insights from the a-priori tests are used to augment existing
slip-based wall models. Various a posteriori tests reveal superior performance
over the dynamic slip wall model. Guidance for the development of improved
slip-wall models is provided, including a target for the dynamic procedure.

Fluid Dynamics