  We introduce a model of interacting singularities of Navier-Stokes, named
pin\,cons. They follow a Hamiltonian dynamics, obtained by the condition that
the velocity field around these singularities obeys locally Navier-Stokes
equations. This model can be seen of a generalization of the vorton model of
Novikov, that was derived for the Euler equations. When immersed in a regular
field, the pin\,cons are further transported and sheared by the regular field,
while applying a stress onto the regular field, that becomes dominant at a
scale that is smaller than the Kolmogorov length. We apply this model to
compute the motion of a dipole of pin\,cons. When the initial relative
orientation of the dipole is inside the interval (0, pi/2), a dipole made of
pin\,con of same intensity exhibits a transient collapse stage, following a
scaling with dipole radius tending to 0 like (tc - t) power 0.63. For long
time, the dynamics of the dipole is however repulsive, with both components
running away from each other to infinity.
