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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 → ω and the vortex stretching vector S → ω, where S is the strain matrix. 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. 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.

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