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 of 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 ar e discussed. Representative values of the apparent deceleration parameter ((q) over tilde) are computed, in order to compare ou r results with the theoretical predictions of the tilted-universe scenario. We conclude that better velocity field reconstructions are necessa r y in order to constrain the parameters implied in LLSS research and alternative cosmologies.