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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.
01/2007: pages 3-26;