  We show that in the variational multiscale framework, the weak enforcement of
essential boundary conditions via Nitsche's method corresponds directly to a
particular choice of projection operator. The consistency, symmetry and penalty
terms of Nitsche's method all originate from the fine-scale closure dictated by
the corresponding scale decomposition. As a result of this formalism, we are
able to determine the exact fine-scale contributions in Nitsche-type
formulations. In the context of the advection-diffusion equation, we develop a
residual-based model that incorporates the non-vanishing fine scales at the
Dirichlet boundaries. This results in an additional boundary term with a new
model parameter. We then propose a parameter estimation strategy for all
parameters involved that is also consistent for higher-order basis functions.
We illustrate with numerical experiments that our new augmented model mitigates
the overly diffusive behavior that the classical residual-based fine-scale
model exhibits in boundary layers at boundaries with weakly enforced essential
conditions.
