  We characterize the peculiar velocity field of the local large-scale
structure reconstructed from the $2M++$ survey, by treating it as a fluid,
extracting the divergence via different approximations over a range pf averaged
scales. This reconstructed field is important for cosmology, since it was used
to correct the peculiar redshifts of the last SNIA compilation Pantheon+. The
results have intriguing implications for the LLSS fluid dynamics and
particularly for the ``Tilted Cosmology'' model, although those results have to
be taken carefully as the velocity field could contain significant bias due to
the reconstruction procedure. Those possible bias and its influence in our
results are discussed. Representative values of the apparent deceleration
parameter ($\Tilde{q}$) are computed, in order to compare our results with the
theoretical predictions of the tilted-universe scenario. We conclude that
better velocity field reconstructions are necessary in order to constrain the
parameters implied in LLSS research and alternative cosmologies.
