  We describe the structure and dynamics of turbulence by the scale-dependent
perceived velocity gradient tensor as supported by following four tracers, i.e.
fluid particles, that initially form a regular tetrahedron. We report results
from experiments in a von K\'arm\'an swirling water flow and from numerical
simulations of the incompressible Navier-Stokes equation. We analyze the
statistics and the dynamics of the perceived rate of strain tensor and
vorticity for initially regular tetrahedron of size $r_0$ from the dissipative
to the integral scale. Just as for the true velocity gradient, at any instant,
the perceived vorticity is also preferentially aligned with the intermediate
eigenvector of the perceived rate of strain. However, in the perceived rate of
strain eigenframe fixed at a given time $t=0$, the perceived vorticity evolves
in time such as to align with the strongest eigendirection at $t=0$. This also
applies to the true velocity gradient. The experimental data at the higher
Reynolds number suggests the existence of a self-similar regime in the inertial
range. In particular, the dynamics of alignment of the perceived vorticity and
strain can be rescaled by $t_0$, the turbulence time scale of the flow when the
scale $r_0$ is in the inertial range. For smaller Reynolds numbers we found the
dynamics to be scale dependent.
