Стаціонарні та рівномірно-обертові конфігурації точкових вихорів

new method, a series of asymmetrical vortex structures was found, which are listed in a catalogue. The majority of the presented asymmetrical vortex structures is new. All of exact initial co-ordinates of vortices are resulted in the cartesian system of co-ordinates both for symmetric and for asymmetrical uniformly rotating vortex structures.

By the method of Runge-Kutta the trajectories of the point vortex configurations are established both without initial perturbations and with small perturbations of the initial positions.

The numerical analysis of Routh’s stability is conducted for all of the presented uniformly rotating point vortex configurations. It is shown that all the symmetric point vortex configurations, presented in Fig.4, are stable when subjected to small perturbations. All asymmetrical configurations (Fig.5 and Fig.6) are unstable with respect to small perturbations of the initial vortex positions.

Key words: point vortex, stationary and uniformly rotating configurations, intensity, Runge-Kutta`s method, trajectories of motion, stability, perturbations of the initial vortex positions.