Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound
Central Institute of Aerohydrodynamics, Acoustic Division, ul. Radio 17, Moscow, 105005, Russian Federation
The state of the art in describing the eigen-oscillations of a vortex ring in an ideal incompressible fluid is reviewed. To describe eigen-oscillations, the displacement field is taken as the basic dynamic variable. A vortex ring with the simplest vorticity distribution in the core and with a potential flow in the vortex ring envelope is the commonest approximation used in treating the eigen-oscillations of vortex rings of a more general form. It turns out that allowing for even a very weak degree of core smoothing causes many oscillation modes to lose their stability. It is shown that the instability effect is determined by the sign of the vibration energy. The energies of the ring eigen-oscillations are calculated and two kinds of eigen-oscillations, those with a negative energy and those with a positive energy, are identified, of which it is the former which become unstable when the core vorticity is smoothed. The multiple instabilities of vortex ring oscillations together with the details of the spatial structure of its eigen-oscillations suggest that it is the nonlinear evolution of precisely these processes which might be the origin of vortex ring turbulence. A new method for the study of unsteady processes in turbulent vortex rings, which utilizes the experimental diagnostics of the ring’s sound field, is presented. The structure of the sound field strongly supports the proposed model of the turbulent vortex ring.