  [abridge]Cosmic velocity and tidal fields are important for the understanding
of the cosmic web and the environments of galaxies, and can also be used to
constrain cosmology. In this paper, we reconstruct these two fields in SDSS
volume from dark matter halos represented by galaxy groups. Detailed mock
catalogues are used to test the reliability of our method against uncertainties
arising from redshift distortions, survey boundaries, and false identifications
of groups by our group finder. We find that both the velocity and tidal fields,
smoothed on a scale of ~2Mpc/h, can be reliably reconstructed in the inner
region (~66%) of the survey volume. The reconstructed tidal field is used to
split the cosmic web into clusters, filaments, sheets, and voids, depending on
the sign of the eigenvalues of tidal tensor. The reconstructed velocity field
nicely shows how the flows are diverging from the centers of voids, and
converging onto clusters, while sheets and filaments have flows that are
convergent along one and two directions, respectively. We use the reconstructed
velocity field and the Zel'dovich approximation to predict the mass density
field in the SDSS volume as function of redshift, and find that the mass
distribution closely follows the galaxy distribution even on small scales. We
find a large-scale bulk flow of about 117km/s in a very large volume,
equivalent to a sphere with a radius of ~170Mpc/h, which seems to be produced
by the massive structures associated with the SDSS Great Wall. Finally, we
discuss potential applications of our reconstruction to study the environmental
effects of galaxy formation, to generate initial conditions for simulations of
the local Universe, and to constrain cosmological models. The velocity, tidal
and density fields in the SDSS volume, specified on a Cartesian grid with a
spatial resolution of ~700kpc/h, are available from the authors upon request.
