TY - JOUR

T1 - Ovsyannikov Vortex in Relativistic Hydrodynamics

AU - Chupakhin, A. P.

AU - Yanchenko, A. A.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - The exact solution of the Euler equations of relativistic hydrodynamics of an compressible fluid—a relativistic analog of the Ovsyannikov vortex (singular vortex) in the classical gas dynamics—was found and investigated. A theorem was proved which shows that the factor system can be represented as 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 were obtained. The stationary solution was studied in detail. It was proved that the invariant subsystem reduces to an implicit differential equation. The branching manifold of the solutions of this equations was studied, and many singular points were found. It is proved that there exist two flow regimes, i.e., the solutions describing the vortex source of a 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.

AB - The exact solution of the Euler equations of relativistic hydrodynamics of an compressible fluid—a relativistic analog of the Ovsyannikov vortex (singular vortex) in the classical gas dynamics—was found and investigated. A theorem was proved which shows that the factor system can be represented as 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 were obtained. The stationary solution was studied in detail. It was proved that the invariant subsystem reduces to an implicit differential equation. The branching manifold of the solutions of this equations was studied, and many singular points were found. It is proved that there exist two flow regimes, i.e., the solutions describing the vortex source of a 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.

KW - group analysis

KW - Ovsyannikov vortex

KW - relativistic hydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=85066633376&partnerID=8YFLogxK

U2 - 10.1134/S0021894419020019

DO - 10.1134/S0021894419020019

M3 - Article

AN - SCOPUS:85066633376

VL - 60

SP - 187

EP - 199

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 2

ER -