  We prove that the vortex structures of solutions to the 3D Navier-Stokes
equations can change their topology without any loss of regularity. More
precisely, we construct smooth high-frequency solutions to the Navier-Stokes
equations where vortex lines and vortex tubes of arbitrarily complicated
topologies are created and destroyed in arbitrarily small times. This instance
of vortex reconnection is structurally stable and in perfect agreement with the
existing computer simulations and experiments. We also provide a
(non-structurally stable) scenario where the destruction of vortex structures
is instantaneous.
