  In this paper, we study the decay rates for the global small smooth solutions
to 3D anisotropic incompressible Navier-Stokes equations. In particular, we
prove that the horizontal components of the velocity field decay like the
solutions of 2D classical Navier-Stokes equations. While the third component of
the velocity field decays as the solutions of 3D Navier-Stokes equations. We
remark that such enhanced decay rate for the third component is caused by the
interplay between the divergence free condition of the velocity field and the
horizontal Laplacian in the anisotropic Navier-Stokes equations.
