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ABSTRACT

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

Thesis for a scientific degree of the candidate of physical and mathematical sciences by speciality 01.04.02. — theoretical physics.— National Taras Shevchenko University of Kyiv, Kyiv, 2005.

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. These solutions nullify the viscous terms in Navier-Stokes equations and grow in time according to an exponential law or by a scenario of non-linear “explosive” instability. The acceleration of the “rigid-body” vortex rotation of an incompressible liquid is due to the joint action of convective and Coriolis forces in the presence of a convergent radial flow, whose velocity is linked by the continuity equation to the intensity of a bulk sink or velocity of an ascending vertical flow, which increases with height. 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 (fireball), 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.

In the case of supersaturated ³Не-⁴Не solutions, it is showed that the formation and growth of hydrodynamic vortices in decomposing ³Не-⁴Не solutions gives rise to quantized vortices in the superfluid component and, as a consequence, leads to acceleration of the process of heterogeneous decomposition (phase separation) in comparison with homogeneous decomposition what was observed experimentally.

In the case of fireball, the prediction that hydrodynamic instability can change the final distributions of the products of nuclear reactions in the phase space was made. Exact axially non-symmetric velocity profiles, which correspond to the elliptic flow, are found. It is also investigated how a finite space-time volume of the fireball (as the region of a bulk sink) effects on the rates of thermal dilepton (e⁺e^-, м⁺м) emission from р⁺р^- meson annihilation processes.

In the case of resonantly excited gas, it is shown that under the conditions of cluster formation the instable behavior of vortex motion can be realized. In contrast, the formation of quasimolecules leads to the stabilization of the rotation inside the gas. The energy of dissociation and typical sizes of quasimolecules are calculated and lifetime is estimated. It is also shown that quasimolecules are metastable. The stationary concentration of quasimolecules in the resonantly excited gas is calculated as a function of laser pumping.

Key words: vortex motion, hydrodynamic instability, stabilization mechanisms, bulk sink, multicomponent system, phase transitions, atmospheric vortices, ³Не-⁴Не solution, hot nuclear matter, resonantly-excited gas.

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