[Show abstract][Hide abstract] ABSTRACT: On the base of the system of hydrodynamic equations we consider a model of formation and development of the hydrodynamic vortices
in the nuclear matter during relativistic heavy-ion collisions, in astrophysical objects, and in powerful atmospheric phenomena
such as typhoons and tornados. A new class of the analytic solutions of non-relativistic hydrodynamic equations for the incompressible
liquid in the presence of a bulk sink are analyzed. The main feature of these solutions is that they describe non-stationary
hydrodynamic vortices with the azimuth component of velocity exponentially or explosively growing with time. A necessary attribute
of a system with such a behavior is a presence of a bulk sink, which provides the existence of the non-stationary vortex regime.
These solutions are obtained by nullifying the terms in the Navier-Stokes equations, which describe viscous effects, exist
and represent vortex structure with “rigid-body” rotation of the core and converging radial flows. With the help of our model
we explain some typical features of the above physical systems from the unique point of view.