Spherization of the velocity field of cosmological perturbations near density extrema

In this work, we consider a mechanism that tends to make the velocity field of linear cosmological perturbations near density extremum points (maxima or minima) spherically symmetric. It is shown that this mechanism begins to operate from the moment the Universe enters the stage of nonrelativistic matter domination ($z<z_{eq}\simeq 3600$) and rather quickly makes the velocity distribution near the density extremum practically isotropic. However, if the density profile of the initial perturbation is noticeably aspherical, its gravitational field subsequently destroys this isotropy.