Vibrations of the vortex ring: turbulence and sound generation in it

The state of the art in describing the natural vibrations of a vortex ring in an ideal incompressible fluid is reviewed. To describe vibrations, 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 how in the atmosphere is the commonest approximation used in treating the vibrations of vortex rings of a more general form. It turns out that allowing for even a very weak degree of core smoothing causes many vibration modes to lose their stability. It is shown that the instability effect is determined by the sign of the vibration energy. The natural vibration energies of the ring are calculated and two kinds of vibrations, 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 instability of vortex ring vibrations together with the details of the spatial structure of its natural vibrations 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 a 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.