A.A.Gourjii Classification of interaction of two axisymmetric Dyson's vortex rings in infinite cylindrical tube |
Applied hydromechanics, Vol. 11 (83) ¹ 3, (2009) |
| The problem on interaction of the system of axisymmetrical vortex rings inside an unbounded cylindrical surface (pipes) filled by an ideal incompressible fluid is considered. Equations of motion of vortices have Hamiltonian structure and two independent invariants of motion, which express the law of impulse conservation along the axis of motion and the law of kinetic energy conservation of ring motion. Researches show that two vortex rings can form a stationary structure which moves with fixed axial velocity along the axis of symmetry. In the case of vortex intensities, which are identical on a sign, rings can participate in single interaction and periodic motion. The system of nonlinear equations, which allows define the region of possible initial parameters of vortices for periodic motion, is formed. Vortex rings with opposite sign of intensities also can move by periodic trajectories. The regions of initial parameters of vortex rings for each of possible types of motion for two axisymmetric vortices with opposite sign of intensities inside a circular pipe filled by an ideal incompressible fluid are drown. |
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| TEXT LANGUAGE: Russian |