1, Universitetskaya str., Izhevsk, 426034, Russia
Udmurt State University
Borisov A. V., Mamaev I. S., Vaskina A. V.
Stability of new relative equilibria of the system of three point vortices in a circular domain
2011, Vol. 7, No. 1, pp. 119-138
This paper presents a topological approach to the search and stability analysis of relative equilibria of three point vortices of equal intensities. It is shown that the equations of motion can be reduced by one degree of freedom. We have found two new stationary configurations (isosceles and non-symmetrical collinear) and studied their bifurcations and stability.
Vaskin V. V., Vaskina A. V., Mamaev I. S.
Problems of stability and asymptotic behavior of vortex patches on the plane
2010, Vol. 6, No. 2, pp. 327-343
With the help of mathematical modelling, we study the dynamics of many point vortices system on the plane. For this system, we consider the following cases:
— vortex rings with outer radius $r = 1$ and variable inner radius $r_0$,
— vortex ellipses with semiaxes $a$, $b$.
The emphasis is on the analysis of the asymptotic $(t → ∞)$ behavior of the system and on the verification of the stability criteria for vorticity continuous distributions.