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Journal of Applied Mechanics and Technical Physics

2014 year, number 2

Steady Vortex Flows of a Self-Gravitating Gas

D. V. Parshin1, A. A. Cherevko1,2, A. P. Chupakhin1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Scinces, Novosibirsk. 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: self-gravitating gas, Ovsyannikov vortex, partly invariant solution, group of rotations, vortex flow of the gas, spherical source


An exact solution of equations of steady motion of a self-gravitating gas is found. This solution describes a vortex flow of the gas from the surface of a spherical source and is partly invariant with respect to the group of rotations (Ovsyannikov vortex, singular vortex). The factor-system of the solution is reduced to finite formulas and one ordinary differential equation of the third order. Various regimes of gas motion described by this solution are determined: unlimited spreading of the gas with swirling from the surface of a spherical source and gas exhaustion with formation of a sphere with elevated density at a finite distance from this source.