This was asked already 3 years ago on stackexchange, see here, but I thought maybe new solutions have become available in the meantime.
For a Navier-Stokes problem with Navier-slip BCs I need to specify $\vec u\cdot\vec n=g$ and $\vec n\cdot\sigma(\vec u, p)\cdot\vec t = f$ or $\vec n\cdot\sigma(\vec u, p)\cdot\vec t + \alpha\vec u\cdot\vec t= 0$, $\vec n$, and $\vec t$ being the normal and tangential (assume 2D) vectors on the boundary.
Is there a manner to specify such BCs directly if $\vec n$, $\vec t$ do not coincide with the cartesian coordinate directions? The answer back then was to use Nitsche's method, i.e., impose the boundary conditions in a weak manner.
In a manual approach one would probably perform local coordinate transformations (rotations) $(\hat x, \hat y) \rightarrow (\vec n, \vec t)$ and impose BCs for $u_n$, $u_t$ directly.
