  We show that certain infinitesimal operators of the Lie-point symmetries of
the incompressible 3D Navier-Stokes equations give rise to vortex solutions
with different characteristics. This approach allows an algebraic
classification of vortices and throws light on the alignment mechanism between
the vorticity and the vortex stretching vector. The symmetry algebra associated
with the Navier-Stokes equations turns out to be infinite- dimensional. New
vortical structures, generalizing in some cases well-known configurations such
as, for example, the Burgers and Lundgren solutions, are obtained and discussed
in relation to the value of the dynamic angle. A systematic treatment of the
boundary conditions invariant under the symmetry group of the equations under
study is also performed, and the corresponding invariant surfaces are
recognized.
