Naryshkin R. Hydrodynamic instability of vortex motion in the systems with a bulk sink of the matter

The thesis is devoted to the origination, development and stabilization processes of instable hydrodynamic vortices in the incompressible liquid. The exact non-stationary solutions of non-linear hydrodynamic equations are investigated in the cylindrical and spherical coordinate systems. Two principal mechanisms of instability: due to bulk sink existence in the multicomponent systems with phase transitions and due to vertical flows with a non-zero velocity gradient are described. The stabilization mechanisms of the hydrodynamic instability are also considered. The general results are applied to the origination of power atmospheric vortices, to the process of decomposition of a supersaturated 3Не-4Не solution, to the rotational motion of the hot nuclear matter, which is formed in relativistic collisions of heavy ions with large angular momenta, and to the resonantly excited gas, in which clusters or quasimolecules (molecules that consist of one non-excited and one excited atom) can be formed. In such systems peculiarities of vortex motion are investigated and mechanisms of bulk sink origination are considered. In some cases the instability of vortex motion helps one to explain existing experimental results or natural phenomena, while in the other cases new effects, which can be tested in experiments, are predicted.