  In this short note, we give a link between the regularity of the solution $u$
to the 3D Navier-Stokes equation, and the behavior of the direction of the
velocity $u/|u|$. It is shown that the control of $\Div (u/|u|)$ in a suitable
$L_t^p(L_x^q)$ norm is enough to ensure global regularity. The result is
reminiscent of the criterion in terms of the direction of the vorticity,
introduced first by Constantin and Fefferman. But in this case the condition is
not on the vorticity, but on the velocity itself. The proof, based on very
standard methods, relies on a straightforward relation between the divergence
of the direction of the velocity and the growth of energy along streamlines.
