Ovsyannikov Vortex in Relativistic Hydrodynamics
A. P. Chupakhin1,2, A. A. Yanchenko1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
Keywords: вихрь Овсянникова, релятивистcкая гидродинамика, групповой анализ, Ovsyannikov vortex, relativistic hydrodynamics, group analysis
Abstract
The exact solution of the Euler equations of relativistic hydrodynamics of an compressible fluid - the relativistic analog of the Ovsyannikov vortex (a special vortex) in the classical gas dynamics. The theorem on the representation of the factor system in the form of a union of a noninvariant subsystem for the function defining the deviation of the velocity vector from the meridian and an invariant subsystem for the function defining thermodynamic parameters, the Lorentz factor, and the radial component of the velocity vector. Compatibility conditions of the overdetermined noninvariant system are obtained. The stationary solution is studied in detail. It is proved that the invariant subsystem reduces to an implicit differential equation. The branching manifold of the solution of this equations was studied, and many singular points were found. The existence of two flow regimes, i.e., solutions describing the vortex source relativistic gas, was proved. One of these solutions is defined only at a finite distance from the source, and the other is an analog of supersonic gas flow from the surface of a sphere.
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