  We present a method for decomposing the cosmological velocity field in a
given volume into its divergent component due to the density fluctuations
inside the volume, and its tidal component due to the matter distribution
outside the volume. The input consists of the density and velocity fields that
are reconstructed either by POTENT or by Wiener Filter from a survey of
peculiar velocities. The tidal field is further decomposed into a bulk velocity
and a shear field. The method is applied here to the Mark III data within a
sphere of radius 60 Mpc/h about the Local Group, and to the SFI data for
comparison. We find that the tidal field contributes about half of the
Local-Group velocity with respect to the CMB, with the tidal bulk velocity
pointing to within ~ 30 degrees of the CMB dipole. The eigenvector with the
largest eigenvalue of the shear tensor is aligned with the tidal bulk velocity
to within ~ 40 degrees. The tidal field thus indicates the important dynamical
role of a super attractor of mass (2-5) x 10^17 M_sun/h Omega^0.4 at ~ 150
Mpc/h, coinciding with the Shapley Concentration. There is also a hint for the
dynamical role of two big voids in the Supergalactic Plane. The results are
consistent for the two data sets and the two methods of reconstruction.
