  We study the regularity criteria for weak solutions to the $3D$
incompressible Navier--Stokes equations in terms of the geometry of vortex
structures, taking into account the boundary effects. A boundary regularity
theorem is proved on regular domains with a class of oblique derivative
boundary conditions, providing that the vorticity of the fluid is coherently
aligned. In particular, we establish the boundary regularity on round balls,
half-spaces and right circular cylindrical ducts, subject to the classical
Navier and kinematic boundary conditions.
