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This article is cited in 1 scientific paper (total in 1 paper)
Ovsyannikov vortex in relativistic hydrodynamics
A. P. Chupakhinab, A. A. Yanchenkoab a Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
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.
Keywords:
Ovsyannikov vortex, relativistic hydrodynamics, group analysis.
Received: 11.10.2018 Revised: 11.10.2018 Accepted: 29.10.2018
Citation:
A. P. Chupakhin, A. A. Yanchenko, “Ovsyannikov vortex in relativistic hydrodynamics”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 5–18; J. Appl. Mech. Tech. Phys., 60:2 (2019), 187–199
Linking options:
https://www.mathnet.ru/eng/pmtf455 https://www.mathnet.ru/eng/pmtf/v60/i2/p5
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