  Affordable, high order simulations of turbulent flows on unstructured grids
for very high Reynolds number flows require wall models for efficiency.
However, different wall models have different accuracy and stability
properties. Here, we develop a kinetic energy stability estimate to investigate
stability of wall model boundary conditions. Using this norm, two wall models
are studied, a popular equilibrium stress wall model, which is found to be
unstable and the dynamic slip wall model which is found to be stable. These
results are extended to the discrete case using the Summation by parts (SBP)
property of the discontinuous Galerkin method. Numerical tests show that while
the equilibrium stress wall model is accurate but unstable, the dynamic slip
wall model is inaccurate but stable.
