  This paper presents the construction of a correct-energy stabilized finite
element method for the incompressible Navier-Stokes equations. The framework of
the methodology and the correct-energy concept have been developed in the
convective--diffusive context in the preceding paper [M.F.P. ten Eikelder, I.
Akkerman, Correct energy evolution of stabilized formulations: The relation
between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric
analysis. I: The convective--diffusive context, Comput. Methods Appl. Mech.
Engrg. 331 (2018) 259--280]. The current work extends ideas of the preceding
paper to build a stabilized method within the variational multiscale (VMS)
setting which displays correct-energy behavior. Similar to the
convection--diffusion case, a key ingredient is the proper dynamic and
orthogonal behavior of the small-scales. This is demanded for correct energy
behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin
(SUPG) and the Galerkin/least-squares method (GLS).
  The presented method is a Galerkin/least-squares formulation with dynamic
divergence-free small-scales (GLSDD). It is locally mass-conservative for both
the large- and small-scales separately. In addition, it locally conserves
linear and angular momentum. The computations require and employ NURBS-based
isogeometric analysis for the spatial discretization. The resulting formulation
numerically shows improved energy behavior for turbulent flows comparing with
the original VMS method.
