  In the Eulerian approach, the motion of an incompressible fluid is usually
described by the velocity field which is given by the Navier--Stokes system.
The velocity field generates a flow in the space of volume-preserving
diffeomorphisms. The latter plays a central role in the Lagrangian description
of a fluid, since it allows to identify the trajectories of individual
particles. In this paper, we show that the velocity field of the fluid and the
corresponding flow of diffeomorphisms can be simultaneously approximately
controlled using a finite-dimensional external force. The proof is based on
some methods from the geometric control theory introduced by Agrachev and
Sarychev.
